01 Key Concepts
Factor
A number that divides another number exactly, with no remainder. Example: 3 is a factor of 12, since 12/3=4 exactly.
Multiple
The result of multiplying a number by any whole number. Example: 12 is a multiple of 3, since 3x4=12.
Finding All Factors
To find every factor of a number, test each whole number up to its square root and pair it with its corresponding co-factor.
Finding Multiples
To list multiples of a number, multiply it by 1, 2, 3, 4, and so on.
Factor Pairs
Two numbers that multiply together to give a specific product, such as 3 and 4 being a factor pair of 12.
02 Solved Examples
Example 1 Find all factors of 18.
- Test whole numbers up to sqrt(18)~4.2: 1, 2, 3, 4.
- 18/1=18, 18/2=9, 18/3=6, 18/4 is not exact.
- Factor pairs: (1,18), (2,9), (3,6).
Answer: Factors of 18: 1, 2, 3, 6, 9, 18
Example 2 List the first 5 multiples of 7.
- Multiply 7 by 1, 2, 3, 4, 5.
- 7, 14, 21, 28, 35.
Answer: 7, 14, 21, 28, 35
Example 3 Is 6 a factor of 42?
- Divide 42 by 6: 42/6 = 7, with no remainder.
Answer: Yes, 6 is a factor of 42
03 Practice Questions
1Find all factors of 20.
1, 2, 4, 5, 10, 20
2List the first 5 multiples of 4.
4, 8, 12, 16, 20
3Is 9 a factor of 45?
Yes, 45/9=5
4Is 7 a factor of 50?
No, 50/7 is not a whole number
5Find all factors of 15.
1, 3, 5, 15
📄 Factors & Multiples — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.