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Britain & the wider world: 1745 -1901
1l the quest for political stability: germany, 1871-1991
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Medieval period: 1066 -1509
2d religious conflict and the church in england, c1529-c1570
2o democracy and nazism: germany, 1918-1945
1f industrialisation and the people: britain, c1783-1885
1c the tudors: england, 1485-1603
2m wars and welfare: britain in transition, 1906-1957
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2s the making of modern britain, 1951-2007
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3
0
Revise Time
07/12/2025
Maths
Factors,LCM and HCF
152
•
7 Dec 2025
•
Understanding prime factors, highest common factors, and lowest common multiples... Show more
Ever wondered how to break down any number into its basic building blocks? That's exactly what prime factors do - they're like finding the DNA of numbers!
An integer is simply a whole number (like 5, 28, or 156). A factor is any positive whole number that divides perfectly into another number without leaving a remainder. When that factor happens to be a prime number, we call it a prime factor.
To find prime factors, you'll use a prime factor tree. Start with your number (like 28), split it into two factors (7 × 4), then keep breaking down any non-prime numbers until you're left with only prime numbers. Circle each prime as you find it - those circled numbers are your prime factors!
Quick Tip: Remember that prime numbers can't be broken down further, so you can stop splitting once you hit them.
For 28, you'd get 2 × 2 × 7, which gives you all the prime building blocks of that number.
Finding what numbers have in common is like discovering shared interests between friends - and that's where the highest common factor comes in handy!
A common factor is any number that divides perfectly into two or more numbers. The highest common factor (HCF) is simply the largest number that fits into all your given numbers without remainders.
You've got two methods to tackle this. Method 1 involves listing all factors of each number, then spotting the highest one they share. Method 2 uses prime factor trees - create them for both numbers, pop the results into a Venn diagram, then multiply the numbers that appear in the overlapping section.
Remember: The HCF will never be larger than the smallest number you're working with.
For 15 and 75, both methods give you 15 as the answer - because 15 fits into both numbers perfectly, and nothing larger will work.
Think of the lowest common multiple as finding the smallest number that both of your original numbers can divide into - it's like finding the first time two different cycles line up perfectly!
A multiple is what you get when you multiply a number by any whole number. Common multiples are multiples that two or more numbers share, and the lowest common multiple (LCM) is the smallest of these shared multiples.
Here's the clever bit: use prime factor trees for both numbers, place all the prime factors in a Venn diagram, then multiply every single number in the diagram together. Unlike finding the HCF where you only multiply the overlapping section, for LCM you multiply absolutely everything.
Top Tip: The LCM is always at least as large as the biggest number you started with.
This method works because you're essentially building the smallest number that contains all the prime factors needed for both original numbers.
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
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 prime factors, highest common factors, and lowest common multiples is essential for solving many maths problems. These concepts help you break down numbers and find connections between them, making calculations much easier.
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Ever wondered how to break down any number into its basic building blocks? That's exactly what prime factors do - they're like finding the DNA of numbers!
An integer is simply a whole number (like 5, 28, or 156). A factor is any positive whole number that divides perfectly into another number without leaving a remainder. When that factor happens to be a prime number, we call it a prime factor.
To find prime factors, you'll use a prime factor tree. Start with your number (like 28), split it into two factors (7 × 4), then keep breaking down any non-prime numbers until you're left with only prime numbers. Circle each prime as you find it - those circled numbers are your prime factors!
Quick Tip: Remember that prime numbers can't be broken down further, so you can stop splitting once you hit them.
For 28, you'd get 2 × 2 × 7, which gives you all the prime building blocks of that number.
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Finding what numbers have in common is like discovering shared interests between friends - and that's where the highest common factor comes in handy!
A common factor is any number that divides perfectly into two or more numbers. The highest common factor (HCF) is simply the largest number that fits into all your given numbers without remainders.
You've got two methods to tackle this. Method 1 involves listing all factors of each number, then spotting the highest one they share. Method 2 uses prime factor trees - create them for both numbers, pop the results into a Venn diagram, then multiply the numbers that appear in the overlapping section.
Remember: The HCF will never be larger than the smallest number you're working with.
For 15 and 75, both methods give you 15 as the answer - because 15 fits into both numbers perfectly, and nothing larger will work.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Think of the lowest common multiple as finding the smallest number that both of your original numbers can divide into - it's like finding the first time two different cycles line up perfectly!
A multiple is what you get when you multiply a number by any whole number. Common multiples are multiples that two or more numbers share, and the lowest common multiple (LCM) is the smallest of these shared multiples.
Here's the clever bit: use prime factor trees for both numbers, place all the prime factors in a Venn diagram, then multiply every single number in the diagram together. Unlike finding the HCF where you only multiply the overlapping section, for LCM you multiply absolutely everything.
Top Tip: The LCM is always at least as large as the biggest number you started with.
This method works because you're essentially building the smallest number that contains all the prime factors needed for both original numbers.
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the essential concepts of number properties, including powers, roots, fractions, factors, and multiples. This summary covers key topics such as exponent rules, laws of indices, and rounding techniques, providing a comprehensive understanding for students. Ideal for quick revision or exam preparation.
MathsExplore 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.
MathsExplore 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.
MathsApp Store
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
Sociology