Factor Calculator
Enter a positive whole number to find all of its factors, matching factor pairs, prime factorization, total number of divisors and the sum of its positive factors.
Factor pairs
1 × 120, 2 × 60, 3 × 40, 4 × 30, 5 × 24, 6 × 20, 8 × 15, 10 × 12
How to use the Factor Calculator
- Enter a positive whole number.
- The calculator checks possible divisors up to the square root of the number.
- When an exact divisor is found, its matching factor pair is added automatically.
- The complete factor list is sorted from smallest to largest.
- Prime factorization repeatedly divides the number by prime factors until no further factor remains.
- The result also shows whether the number is prime or composite, the total factor count and the sum of all positive factors.
Examples
Factors of 12
The positive factors of 12 are 1, 2, 3, 4, 6 and 12. Its factor pairs are 1 × 12, 2 × 6 and 3 × 4.
Factors of 36
The positive factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
Prime factorization of 120
120 = 2 × 2 × 2 × 3 × 5, which can also be written as 2³ × 3 × 5.
Prime number example
13 has only two positive factors, 1 and 13, so it is a prime number.
Frequently asked questions
What is a factor of a number?
A factor is a whole number that divides another whole number exactly with no remainder.
What are factor pairs?
Factor pairs are two whole numbers that multiply together to equal the original number. For example, 3 and 4 are a factor pair of 12.
What is prime factorization?
Prime factorization expresses a whole number as a product of prime numbers. For example, 60 = 2 × 2 × 3 × 5.
Is 1 a prime number?
No. A prime number has exactly two positive factors, 1 and itself. The number 1 has only one positive factor.
How do I find all factors efficiently?
Check divisors only up to the square root of the number. Every exact divisor below the square root has a matching factor above it.
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