### Factors:

The factors of a number are the whole numbers that divide the number without any remainder. e.g. the factors of 18 may be found as follows:

Factors of 18 are 1, 2, 3, 6, 9, 18

### Multiples:

A multiple of a whole number is obtained by multiplying it by any whole number e.g.

The multiples of 4 are

4 x 1, 4 x 2, 4 x 3, 4 x 4, 4 x 5, 4 x 6 …..

which are 4, 8, 12, 16, 20, 24, …. etc

Example 1

**a.** Find all the factors of 36

**b.** State which of these factors are even

**c**. State which of these factors are odd

**Solution**

a. Factors of 36 = 1, 2, 3, 4, 9, 12, 18 and 36

b. Even numbers are 2, 4, 12, 18 and 36

c. Odd numbers are 1, 3 and 9

Example 2

**a.** Write the first five multiples of 12

**b. **Which of them are multiples of 8

**Solution**

a. Multiples of 12 are

12 x 1 = 12

12 x 2 = 24

12 x 3 = 36

12 x 4 = 48

12 x 5 = 60

Multiples of 12 are 12, 24, 36, 48 and 60

b. The multiples of 8 in 12, 24, 36, 48 and 60

are 24 and 48

because ;

24 = 3 x 8

48 = 8 x 6

### Prime Number:

A prime number is a number that can only be divided by 1 and itself. It has only two factors.

Examples are;

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 91, 97 etc.

### Prime factor:

A prime factor is a factor that is also a prime number e.g

The factors of 20 are 1, 2, 4, 5, 10, and 20.

Out of these the prime factors of 18 are 2 and 5.

### Product of Prime factors:

A given number can be expressed as a product of its prime factors. This is achieved by successive or repeated division by prime factors.

Example 3

Express the following numbersas a product of their prime factors. Express your answer in index form.

**(a) **36

**(b)** 320

**(c)** 336

**Solution**

**(a)**36

36 = 2 x 2 x 3 x 3 = 2^{2} x 3^{2}

**(b)**320

320 = 2 x 2 x 2 x 2 x 2 x 2 x 5 = 2^{6} x 5

**(c)** 336

336 = 2 x 2 x 2 x 2 x 3 x 7 = 2^{4} x 3 x 7