Multiples

If a number divides exactly into another number, the second is a multiple of the first.

Example 3, 6, 9, 12, 15, 18 are the first six multiples of 3 Example 10, 12, 14, 16, 18, 20 are the set of multiples of 2 between 10 and 20 inclusive

Example From the set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Write down the multiples of (i) 2 (ii) 4 (iii) 6

Lowest Common Multiple (LCM)

Example Find the lowest common multiple of 12 and 15. That is the smallest common multiple of the two numbers

Example Find the lowest common multiple of 9 and 12.

Factors

A factor is a number that will divide exactly into a given number Example List all the factors of (i) 6 (ii) 12 (iii) 30 (iv) 19

Prime numbers

A prime number is a number that can be divided exactly by itself and one only.

In other words it has only two factors Example List the first 8 prime numbers.

Prime Factors

When we want to express a number as a product of its prime factors we express the number as a multiplication of prime numbers Example Express 48 in terms of its prime factors

Example Express each of the following as products of prime numbers a) 100 b) 42 c) 72 d) 84 e) 144

Highest common factor (HCF)

The highest common factor of two or more numbers is the greatest number which will divide exactly into each of them.

Example Find the HCF of 4, 6 and 8

Example Find the HCF of a) 6, 9 and 12 b) 12 and 18