Factors Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Factors.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Whole numbers that divide evenly into a given number with no remainder—the 'building blocks' that multiply together to make it.
Factors are the 'building blocks' you multiply together to make a number.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Every number can be broken into factors; primes are the ultimate factors.
Common stuck point: Students forget 1 and the number itself are always factors, or stop searching before finding all factor pairs.
Sense of Study hint: Systematically test 1, 2, 3, ... up to the square root of the number. Each time one divides evenly, you get a factor pair.
Worked Examples
Example 1
easySolution
- 1 Test divisors from 1 up to \sqrt{56} \approx 7.5: 56 \div 1 = 56, 56 \div 2 = 28, 56 \div 4 = 14, 56 \div 7 = 8.
- 2 56 \div 3, 56 \div 5, and 56 \div 6 are not whole numbers.
- 3 Factors: \{1, 2, 4, 7, 8, 14, 28, 56\}.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
easyBackground Knowledge
These ideas may be useful before you work through the harder examples.