Factor Calculator
Enter any positive integer and get all of its factors in one click. The calculator lists every factor, shows factor pairs, counts them, adds them up, and tells you whether the number is prime. Try 60 and you will see 12 factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
What Is a Factor?
A factor of a number is any integer that divides it evenly (with no remainder). For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Finding Factors
Start at 1 and test each integer up to the square root of the number. Each time you find a factor, its pair (the number divided by that factor) is also a factor. For 36: testing 1 through 6 gives pairs (1, 36), (2, 18), (3, 12), (4, 9), (6, 6).
Factor Pairs
Factor pairs are two numbers that multiply together to produce the original number. The number 24 has factor pairs: (1, 24), (2, 12), (3, 8), (4, 6).
Prime Numbers
A prime number has exactly two factors: 1 and itself. Numbers like 2, 3, 5, 7, 11, and 13 are prime. The number 1 is a special case and is considered neither prime nor composite.
Sum of Factors
The sum of all factors (also called the sigma function) has uses in number theory. If the sum of a number's proper factors (all factors except itself) equals the number, it is called a perfect number. For example, 6 = 1 + 2 + 3.