HCF stands for Highest Common Factor, which is the largest number that divides exactly into 2 or more numbers. An example of this is the HCF of 12 and 20, which is 4. On the other hand, LCM stands for Lowest Common Multiple, and it is the smallest number that is in the times table of 2 or more numbers. For instance, the LCM of 12 and 20 is 60.
Product of Prime Factors
This involves finding all the prime numbers that would multiply to give the number. It is often shown using a factor tree, and an example of this is when 40 is expressed as 2³x5.
Finding HCF and LCM
When finding the HCF and LCM of two numbers such as 24 and 60, the process involves expressing the numbers as the product of their prime factors. For instance,
24 = 2x2x2x3 = 2³x3
60 = 2x2x8x5 = 2²×3×5
Therefore, the HCF of 24 and 60 is 12, and the LCM of the same numbers is 120.
The law of indices states that when multiplying indices with the same base, you add the indices, and when dividing indices with the same base, you subtract the indices. Additionally, when raising a power to a power, you multiply the indices. Also, anything to the power of 0 equals 1, and nothing gets multiplied. Finally, a negative sign means one over the base number.
A number in standard form is expressed as A x 10h, where 1≤ A < 10. This form is used for writing very small or very large numbers out easily. An example of this is 6720000 = 6.72×10⁶.
A surd is a number written exactly using square or cube roots. For instance, √2 and √5 are surds. However, √4 and ∛27 are not surds. The law of surds states that √a × √a = a, and √a × √b = √ab. Additionally, ∛a × ∛a = a, and ∛a × ∛b = ∛ab.
