Summary

1. If a number is divisible by another, the second number is called a factor of the first. For example, 4 is a factormultiple of 12 because 12 is divisible by (12 ÷ 4 = ).

2. numbers are numbers like 2, 3, 5, 7, 11, … that have only twoone factors, namely and themselves.

3. numbers are numbers like 4, 6, 8, 9, … that have more than 21 factors, i.e., at least one factor other than and themselves. For example, 8 has the factor and 9 has the factor , so 8 and 9 are both composite.

4. Every number greater than 1 can be written as a of prime numbers. This is called the number's prime factorisation. For example, 84 = 2 × 2 × 3 × .

5. There is only onetwo way to factorise a number into , except for the ordering of the factors.

6. Two numbers that do not have a factor other than are said to be co-primeprime.

7. To check if two numbers are co-prime, we can first find their prime factorisations and check if there is a prime factor. If there is no common prime factor, they are co-prime, and otherwise they are not.

8. A number is a factor of another number if the prime factorisation of the first number is included in the prime factorisation of the number.