In mathematics, a factor is a number that divides another number exactly, with no remainder.

Simple definition

A number A is a factor of a number B if:

B ÷ A = a whole number (integer)

Example

Take the number 12.

Numbers that divide 12 evenly are:

• 1 → 12 ÷ 1 = 12

• 2 → 12 ÷ 2 = 6

• 3 → 12 ÷ 3 = 4

• 4 → 12 ÷ 4 = 3

• 6 → 12 ÷ 6 = 2

• 12 → 12 ÷ 12 = 1

✅ So, the factors of 12 are:
1, 2, 3, 4, 6, 12

Important things to know about factors

1. Every number has at least two factors

• 1 (always a factor)

• The number itself

Example:
Factors of 7 → 1 and 7

2. Prime vs Composite numbers

• Prime number: has exactly two factors

  • Example: 2, 3, 5, 7, 11

• Composite number: has more than two factors

  • Example: 4, 6, 8, 12

3. Factor pairs

Factors often come in pairs that multiply to give the number.

Example (18):

• 1 × 18

• 2 × 9

• 3 × 6

4. Factors vs multiples

• Factors divide a number

• Multiples are the result of multiplying a number

Example (6):

• Factors: 1, 2, 3, 6

• Multiples: 6, 12, 18, 24, …