Factor Calculator
Enter any positive integer to instantly find all of its factors and factor pairs.
Result
Factors of :
Factor Pairs
These pairs multiply together to equal your number.
Step-by-Step Solution
To find all factors, we check every number starting from 1 up to the square root of your number. If it divides evenly, we find a pair.
What is a Factor?
A factor is a whole number that divides another number exactly, leaving no remainder.
For example, let's look at the number 12:
- 12 ÷ 1 = 12
- 12 ÷ 2 = 6
- 12 ÷ 3 = 4
Since 1, 2, 3, 4, 6, and 12 all divide 12 perfectly, they are all factors of 12.
Prime vs. Composite Numbers
The number of factors tells you if a number is Prime or Composite:
- Prime Number: Has exactly two factors: 1 and itself. (e.g., 2, 3, 5, 7, 11)
- Composite Number: Has more than two factors. (e.g., 4, 6, 8, 9, 10)
- Special Case: The number 1 has only one factor (itself), so it is neither prime nor composite.
Frequently Asked Questions
How do I find factors of a large number?
Start dividing by 1, then 2, then 3, and so on. For every number that divides evenly, you actually find two factors (the divisor and the answer). Stop when your divisor is larger than the square root of the number.
What is a "Proper Divisor"?
Proper divisors are all the factors of a number except the number itself. For example, the proper divisors of 6 are 1, 2, and 3 (but not 6).
Why are factors important?
Factors are the building blocks of math. They are used to simplify fractions, find common denominators, solve algebraic equations, and encrypt data (cryptography).