Factors and Factor Pairs

What Is a Factor?

A factor of a number divides evenly into that number (no remainder).

Factors of 12: 1, 2, 3, 4, 6, 12 Because: $12 \div 1 = 12$, $12 \div 2 = 6$, $12 \div 3 = 4$, etc.

Factor Pairs

Factors come in pairs that multiply to give the number:

Factor pairs of 24: $(1, 24)$, $(2, 12)$, $(3, 8)$, $(4, 6)$

Finding All Factors

Start dividing by 1, 2, 3, 4, ... Stop when the pairs start repeating.

Example: Find all factors of 36

• $36 \div 1 = 36$ → pair $(1, 36)$
• $36 \div 2 = 18$ → pair $(2, 18)$
• $36 \div 3 = 12$ → pair $(3, 12)$
• $36 \div 4 = 9$ → pair $(4, 9)$
• $36 \div 6 = 6$ → pair $(6, 6)$

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Prime and Composite Numbers

• Prime number: Has exactly 2 factors (1 and itself). Examples: 2, 3, 5, 7, 11, 13
• Composite number: Has more than 2 factors. Examples: 4, 6, 8, 9, 10, 12
• 1 is neither prime nor composite

Multiples

A multiple of a number is the product of that number and any whole number.

Multiples of 5: 5, 10, 15, 20, 25, 30, ...

Remember: Every number is a factor of itself and a multiple of itself.