A factor calculator helps identify whole numbers that divide a given integer without leaving a remainder. Factors are useful in arithmetic, simplifying fractions, and finding the greatest common factor (GCF).
What are factors?
A positive factor of a positive integer n is a positive integer that divides n exactly. For example, the positive factors of 12 are 1, 2, 3, 4, 6, and 12. Each divides 12 with remainder zero.
How to use a factor calculator
- Open the Factor Calculator.
- Enter a positive whole number.
- Calculate its factors.
- Check the result by dividing the original number by any listed factor.
How to find factors manually
Test positive integers from 1 up to the square root of the number. Whenever a candidate divides evenly, record both the candidate and its partner. For 36, the pairs are 1 × 36, 2 × 18, 3 × 12, 4 × 9, and 6 × 6. The distinct positive factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors vs multiples
Factors divide a number exactly, while multiples are formed by multiplying a number by integers. For instance, 3 is a factor of 12, whereas 12, 24, and 36 are multiples of 12.
Common factor examples
| Number | Positive factors |
|---|---|
| 10 | 1, 2, 5, 10 |
| 15 | 1, 3, 5, 15 |
| 20 | 1, 2, 4, 5, 10, 20 |
| 28 | 1, 2, 4, 7, 14, 28 |
Using factors to find the GCF
To find the greatest common factor of 18 and 24, list their factors. Factors of 18 are 1, 2, 3, 6, 9, 18. Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The greatest shared factor is 6.
Prime vs composite numbers
A prime number has exactly two positive factors: 1 and itself. A composite number has more than two. The number 1 is neither prime nor composite.
Common mistakes
- Confusing factors with multiples.
- Forgetting factor pairs.
- Assuming every number has many factors; primes have exactly two positive factors.
- Calling 1 a prime number.
Frequently asked questions
What are the factors of 24?
1, 2, 3, 4, 6, 8, 12, and 24.
Is 1 a factor of every positive integer?
Yes.
Can factors be negative?
Yes, integers have negative divisors too. Factor lists in basic arithmetic often show only positive factors.
How can I quickly check a factor?
Divide the original integer by the candidate. If the quotient is an integer, it is a factor.
Use the Factor Calculator to verify the factors of your chosen number.
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