N4: use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem

What are prime numbers?

Numbers which have only two factors, themselves and 1, such as 19

What are factors?

A number that divides another with no remainder - 2 is a factor of 4 because when 2 divides 4, it leaves 2 groups of 2

What are multiples?

A multiple is one of the numbers you get when you multiply a certain number by an integer; multiples of 5 are 5, 10, 15, 20 etc

What are lowest common multiples (LCM)?

When you have two numbers, the LCM is the smallest number that is a multiple of both; the LCM of 35 and 10 is 70, because 70 is 7×10 and 2×35

How to calculate LCM

Use a prime factor tree for each number, then pair as many of those factors as possible. For each pair, only use one of the numbers, but use each unpaired number in the final calculation. Multiply the factors to find the LCM

LCM of 28 and 35

140

What are common multiples?

All of the numbers which are multiples of two larger numbers

Give an example of common multiples with 5 and 7

While the LCM of 5 and 7 is 35, other common multiples are 70, 105, 140 (the LCM is multiplied)

What is a prime factor tree?

A ‘tree’ diagram used to find prime factors of a number

Find the prime factors of 250

2×5³

What is the highest common factor (HCF)?

The largest factor of two numbers

How to find HCF

Use prime factor trees and a Venn diagram. Plot all prime factors within the diagram and multiply all that are in the middle segment

Find HCF of 48 and 60

12

What are common factors?

These are factors that are found within both numbers

What are the common factors of 10 and 15?

1 and 5 (because 2, 3, 10 and 15 are all factors but do not fit into both - 1 will always be a factor)

What is product notation?

Prime factors can be expressed in two ways; 2×2×2×3×3×4 or 2³x3²x4 - the latter is product notation (the product has notation involved)

What is the unique factorisation theorem?

It states that the prime factorisation of a number will always have the same outcome, no matter how it is reached