This free online factor calculator lists every factor of a positive integer and breaks it down into its prime factorization. It's a handy tool for finding common factors, checking divisibility, or studying number theory.
How to Use the Factor Calculator
Enter a positive whole number in the "Number" field.
Click "Calculate" to see the full list of factors.
Check the "Prime Factorization" line to see the number expressed as a product of primes.
Factor Pairs: Why Checking up to the Square Root Is Enough
Factors come in pairs that multiply to give the number. For 60, the pairs are 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12 and 6 × 10. The square root of 60 is about 7.75, and in every pair one factor is at or below that point and the other is above it. So once you have tested 1 to 7, you have found every pair, and the full list of twelve factors follows. For a perfect square such as 36, the middle pair is 6 × 6, and 6 is listed only once.
Finding the Prime Factorization by Repeated Division
The calculator divides by 2 as many times as it can, then by 3, then 4, 5 and so on. Composite divisors such as 4 never actually divide at that stage, because their prime parts have already been removed. Whatever is left at the end, if larger than 1, is itself a prime. For 360:
360 ÷ 2 = 180, 180 ÷ 2 = 90, 90 ÷ 2 = 45. That is three 2s.
45 ÷ 3 = 15, 15 ÷ 3 = 5. That is two 3s.
5 is prime, so the result is 360 = 2^3 × 3^2 × 5.
The exponents also tell you how many factors a number has without listing them: add 1 to each exponent and multiply. For 360 that is (3 + 1) × (2 + 1) × (1 + 1) = 24 factors.
Factors of Common Numbers
Number
Prime factorization
Number of factors
12
2^2 × 3
6
36
2^2 × 3^2
9
60
2^2 × 3 × 5
12
97
97 (prime)
2
100
2^2 × 5^2
9
360
2^3 × 3^2 × 5
24
1001
7 × 11 × 13
8
5040
2^4 × 3^2 × 5 × 7
60
Numbers with many factors, such as 60 and 360, are convenient for dividing things evenly, which is often given as the reason for 60 minutes in an hour and 360 degrees in a circle.
Using Factors in Homework and Everyday Problems
HCF and LCM: factorise both numbers. The HCF uses each common prime at its lowest power; the LCM uses every prime at its highest power. For 84 = 2^2 × 3 × 7 and 120 = 2^3 × 3 × 5, the HCF is 2^2 × 3 = 12 and the LCM is 2^3 × 3 × 5 × 7 = 840.
Simplifying fractions: divide the top and bottom by their HCF. 84/120 becomes 7/10 after dividing both by 12.
Testing for a prime: a number is prime when its only factors are 1 and itself, so the list shows exactly two entries.
Spotting perfect squares: only perfect squares have an odd number of factors, because their square root pairs with itself.
Arranging items: to set out 48 chairs in equal rows, each factor pair (such as 6 × 8 or 4 × 12) is one possible layout.
Frequently Asked Questions
It checks every integer from 1 up to the square root of your number. Whenever it finds a divisor i, it records both i and n / i as factors, which is much faster than checking every number up to n. For example, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Prime factorization expresses a number as a product of prime numbers. The calculator repeatedly divides your number by the smallest possible prime until only 1 remains. For example, 60 = 2^2 × 3 × 5.
Factoring is only defined for positive whole numbers, so the calculator requires a positive integer and shows "Please enter a positive integer" otherwise. Numbers above 10,000,000 are also rejected with "Number too large" to keep the calculation fast.
No. A prime has exactly two different factors, 1 and itself, and 1 has only one factor. That is why the calculator reports that 1 has no prime factors. Excluding 1 also keeps every number's prime factorization unique.
Factors divide into a number exactly, so there are only a limited number of them, all no larger than the number itself. Multiples are what you get by multiplying the number by 1, 2, 3 and so on, so they go on forever. For 12, the factors are 1, 2, 3, 4, 6 and 12, while the multiples are 12, 24, 36, 48 and so on.