Factors and Multiples

factor

A number that divides into another number with no remainder. Example: the factors of 12 are 1, 2, 3, 4, 6 and 12.

multiple

The result of multiplying a number by any natural number. Example: the multiples of 3 are 3, 6, 9, 12, 15, 18, …

prime number

A natural number with exactly two factors: 1 and itself. Example: 11 (factors 1 and 11).

composite number

A natural number with more than two factors. Example: 12 (factors 1, 2, 3, 4, 6 and 12).

fundamental theorem of arithmetic

Every composite number can be written as a product of prime numbers. Example: 12 = 2 × 2 × 3 = 2² × 3.

highest common factor (HCF)

The largest number that is a factor of all the given numbers.

lowest common multiple (LCM)

The smallest number that is a multiple of all the given numbers.

HCF and LCM rule

The product of two numbers equals the product of their HCF and LCM.

factors of 12

1, 2, 3, 4, 6 and 12

first six multiples of 3

3, 6, 9, 12, 15, 18

first ten prime numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Is 1 a prime number?

No. It has only one factor, and a prime number needs exactly two.

Is 2 a prime number?

Yes. Its factors are 1 and 2. It is the only even prime number.

Check the HCF and LCM rule for 12 and 18

HCF = 6 and LCM = 36. 12 × 18 = 216 and 6 × 36 = 216.