Ever wondered how numbers relate to each other or why... Show more
SociologySign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
316
•
12 Dec 2025
•
Understanding the Properties of Numbers
Olamide
@olamide_26
Factors, Multiples and Prime Numbers
Factors are numbers that divide exactly into another number without leaving a remainder. Think of them as the building blocks of numbers - like how 2 and 3 are factors of 6 because 2×3=6.
The Highest Common Factor (HCF) is the biggest number that divides into two or more numbers. Multiples are what you get from times tables - so multiples of 5 are 5, 10, 15, 20, etc. The Lowest Common Multiple (LCM) is the smallest number that appears in the times tables of all your given numbers.
Prime numbers only have exactly two factors: themselves and 1. Remember, 1 isn't prime because it only has one factor! The first few primes are 2, 3, 5, 7, 11, 13. When you break numbers down into prime factors, you're finding which primes multiply together to make your original number.
Quick Tip: Always write factors in pairs - it makes finding all of them much easier!
Powers and Indices
Square numbers come from multiplying a number by itself, like 5×5=25. Cube numbers involve multiplying three times: 4×4×4=64. The square root and cube root work backwards - asking "what number gives me this when squared or cubed?"
When working with powers (indices), there are three key rules to master. For multiplication with the same base, you add the powers: a⁵ × a³ = a⁸. For division, you subtract: a⁷ ÷ a² = a⁵. When raising a power to another power, you multiply them: (a³)⁴ = a¹².
Don't confuse x² with 2x! Squaring means multiplying by itself, not by 2. Also remember that any number to the power of 1 equals itself, and any number to the power of 0 equals 1.
Watch Out: p³ when p=2 gives you 2×2×2=8, not 2×3=6!
Fractions Fundamentals
A fraction shows division - the numerator (top number) divided by the denominator (bottom number). Unit fractions have 1 on top, like ½ or ¼.
To simplify fractions, divide both top and bottom by their highest common factor. Equivalent fractions represent the same value: ½ = 2/4 = 10/20. When comparing fractions, convert them to have the same denominator first.
For adding or subtracting fractions, find the LCM of the denominators to create a common denominator. Convert each fraction, then add or subtract only the numerators whilst keeping the denominator the same.
Remember: When rounding money, always show two decimal places - write £27.40, not £27.4!
Rounding and Estimating
Rounding makes numbers easier to work with whilst keeping their value close to the original. If the digit after your rounding position is 5 or more, round up; if it's less than 5, round down.
Significant figures are the meaningful digits in a number. The first significant figure can't be zero, and trailing zeros in decimals don't count. When estimating calculations, round each number to 1 significant figure first.
Decimal places count positions after the decimal point. Always check if you need a specific number of decimal places in your answer, especially with money questions.
Pro Tip: For quick estimates, use the ≈ symbol meaning "approximately equal to" - it shows you're estimating, not calculating exactly!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content: Operations on Fractions
Most popular content in Maths
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Understanding the Properties of Numbers
Olamide
@olamide_26
Ever wondered how numbers relate to each other or why calculators give you weird decimal answers? This maths knowledge organiser covers the essential building blocks you'll use throughout your studies - from finding factors and multiples to working with powers... Show more
Factors, Multiples and Prime Numbers
Factors are numbers that divide exactly into another number without leaving a remainder. Think of them as the building blocks of numbers - like how 2 and 3 are factors of 6 because 2×3=6.
The Highest Common Factor (HCF) is the biggest number that divides into two or more numbers. Multiples are what you get from times tables - so multiples of 5 are 5, 10, 15, 20, etc. The Lowest Common Multiple (LCM) is the smallest number that appears in the times tables of all your given numbers.
Prime numbers only have exactly two factors: themselves and 1. Remember, 1 isn't prime because it only has one factor! The first few primes are 2, 3, 5, 7, 11, 13. When you break numbers down into prime factors, you're finding which primes multiply together to make your original number.
Quick Tip: Always write factors in pairs - it makes finding all of them much easier!
Powers and Indices
Square numbers come from multiplying a number by itself, like 5×5=25. Cube numbers involve multiplying three times: 4×4×4=64. The square root and cube root work backwards - asking "what number gives me this when squared or cubed?"
When working with powers (indices), there are three key rules to master. For multiplication with the same base, you add the powers: a⁵ × a³ = a⁸. For division, you subtract: a⁷ ÷ a² = a⁵. When raising a power to another power, you multiply them: (a³)⁴ = a¹².
Don't confuse x² with 2x! Squaring means multiplying by itself, not by 2. Also remember that any number to the power of 1 equals itself, and any number to the power of 0 equals 1.
Watch Out: p³ when p=2 gives you 2×2×2=8, not 2×3=6!
Fractions Fundamentals
A fraction shows division - the numerator (top number) divided by the denominator (bottom number). Unit fractions have 1 on top, like ½ or ¼.
To simplify fractions, divide both top and bottom by their highest common factor. Equivalent fractions represent the same value: ½ = 2/4 = 10/20. When comparing fractions, convert them to have the same denominator first.
For adding or subtracting fractions, find the LCM of the denominators to create a common denominator. Convert each fraction, then add or subtract only the numerators whilst keeping the denominator the same.
Remember: When rounding money, always show two decimal places - write £27.40, not £27.4!
Rounding and Estimating
Rounding makes numbers easier to work with whilst keeping their value close to the original. If the digit after your rounding position is 5 or more, round up; if it's less than 5, round down.
Significant figures are the meaningful digits in a number. The first significant figure can't be zero, and trailing zeros in decimals don't count. When estimating calculations, round each number to 1 significant figure first.
Decimal places count positions after the decimal point. Always check if you need a specific number of decimal places in your answer, especially with money questions.
Pro Tip: For quick estimates, use the ≈ symbol meaning "approximately equal to" - it shows you're estimating, not calculating exactly!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
9
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Mock Exam
Quiz
Flashcards
Essay
Similar content
LCM and HCF Explained
Explore the concepts of Lowest Common Multiple (LCM) and Highest Common Factor (HCF) with detailed methods for calculation, including prime factorization and Venn diagrams. This summary covers key terms, example problems, and step-by-step solutions to help you master these essential number system concepts. Ideal for students preparing for exams or seeking to strengthen their understanding of factors.
Maths7
Understanding Multiples & Factors
Explore the concepts of multiples, factors, and prime numbers in this comprehensive summary. Learn how to identify multiples through times tables, find all factors of a number, and understand the definition of prime numbers. Ideal for students looking to strengthen their math skills in factoring and number theory.
Maths7
Understanding Factors & Multiples
Explore the concepts of factors, multiples, and prime factorisation in this comprehensive overview. Learn how to identify multiples, determine factor pairs, and perform prime factorisation with clear examples. Ideal for students seeking to strengthen their foundational math skills. This summary lays the groundwork for further topics like HCF and LCM.
Maths7
Most popular content: Operations on Fractions
Most popular content in Maths
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user