FactorFinder

Factors Calculator

Every divisor of n, listed clearly.

Number

Divisors of 60

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

12 divisors total

Prime factorisation: 2 · 2 · 3 · 5

What you entered

Number: 60

1
Test every integer from 1 to n for divisibility
n = 60= 12 divisors found
2
Divisors
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60= 12 total
3
Prime factorization
2 × 2 × 3 × 5= = 60

Result

Divisors found: 12

60 has 12 divisors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Its prime factorization is 2 × 2 × 3 × 5.

All divisors of common numbers

Divisors are every whole number that divides the input with no remainder. The prime factorisation is shown alongside.

Number	Divisors	How many	Prime factorisation
12	1, 2, 3, 4, 6, 12	6	2 x 2 x 3
24	1, 2, 3, 4, 6, 8, 12, 24	8	2 x 2 x 2 x 3
28	1, 2, 4, 7, 14, 28	6	2 x 2 x 7
36	1, 2, 3, 4, 6, 9, 12, 18, 36	9	2 x 2 x 3 x 3
60	1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60	12	2 x 2 x 3 x 5
100	1, 2, 4, 5, 10, 20, 25, 50, 100	9	2 x 2 x 5 x 5

The count of divisors follows directly from the prime factorisation: add one to each exponent and multiply. 60 is 2 squared times 3 times 5, so (2+1)(1+1)(1+1) = 12 divisors, which is why 60 was chosen as the base for minutes and degrees - it divides evenly more ways than any smaller number. 36 and 100 have an odd number of divisors because both are perfect squares, where the square root pairs with itself rather than with a distinct partner. 28 is a perfect number: its divisors excluding itself sum to 28.

Every way a number divides evenly

A factor (or divisor) of n is any number that divides it with no remainder — 12's factors are 1, 2, 3, 4, 6, and 12, found simply by testing every integer up to n.

Why it's useful

Finding common factors is the basis for simplifying fractions, splitting a group evenly (into how many equal teams can 24 people be divided?), and understanding a number's structure via its prime factorisation.

Frequently asked questions

How do I find all factors of a number?

Test every integer from 1 to √n. Each time i divides n evenly, both i and n/i are factors. For 36: test 1-6. Factors found: 1,36; 2,18; 3,12; 4,9; 6,6. Full list: 1, 2, 3, 4, 6, 9, 12, 18, 36.

How many factors does a number have?

From the prime factorization, multiply (each exponent + 1). For 360 = 2³ × 3² × 5¹: (3+1)(2+1)(1+1) = 24 factors. This formula counts every combination of prime powers that divides the number.

What is the difference between a factor and a multiple?

Factors divide INTO the number (factors of 12: 1,2,3,4,6,12). Multiples are the number multiplied OUT (multiples of 12: 12,24,36,48...). Factors are finite; multiples are infinite. 3 is a factor of 12, and 12 is a multiple of 3.