Factor Calculator

Find all factors of a number, prime factorization, factor pairs, and more. Understand the divisibility properties of any positive integer.

Factors

Number of Factors

12

Composite number

All Factors1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Prime Factorization2^2 × 3 × 5
Sum of Factors168

60 is a composite number

Enter a Number

Enter a positive integer to find all its factors.

All Factors of 60

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

Highlighted factors are prime numbers

Factor Pairs

Each pair of factors multiplies to give 60:

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

Prime Factorization

60=2^2 × 3 × 5

Step-by-Step Breakdown:

60÷2=30
30÷2=15
15÷3=5
5÷5=1

Prime factors: 2, 3, 5

Number Properties

Type

Composite

Factor Count

12

Sum of Factors

168

Perfect Square?

No

Sum of proper divisors (excluding 60)

108

60 is an abundant number (less than sum of proper divisors)

Divisibility Check

2
3
4
5
6
7
8
9
10
11
12
13
15
16
17
19
20
25

Green indicates 60 is divisible by that number.

Factors

Number of Factors

12

Composite number

All Factors1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Prime Factorization2^2 × 3 × 5
Sum of Factors168

60 is a composite number

?How to Find Factors of a Number

To find all factors of a number, start from 1 and check each integer up to the square root. If a number divides evenly, both it and the quotient are factors. For example, factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factor pairs multiply to give the original number: 1x36, 2x18, 3x12, 4x9, 6x6.

What is a Factor?

A factor (or divisor) is a number that divides evenly into another number with no remainder. Finding factors is fundamental to understanding number theory, simplifying fractions, finding GCF and LCM, and solving various mathematical problems. Factors always come in pairs that multiply to give the original number.

Key Facts About Factors

  • A factor is a number that divides evenly into another with no remainder
  • Prime factors are factors that are prime numbers (divisible only by 1 and themselves)
  • Every number can be expressed as a product of prime factors (prime factorization)
  • Factor pairs are two factors that multiply to give the original number
  • A perfect number equals the sum of its proper factors (excluding itself)
  • Perfect squares have an odd number of factors
  • The number 1 is a factor of every positive integer
  • Prime numbers have exactly two factors: 1 and themselves

Quick Answer

To find all factors of a number, start from 1 and check each integer up to the square root. If a number divides evenly, both it and the quotient are factors. For example, factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factor pairs multiply to give the original number: 1x36, 2x18, 3x12, 4x9, 6x6.

Frequently Asked Questions

A factor is a number that divides evenly into another number with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each divides 12 with no remainder.
Prime factors are factors that are prime numbers (only divisible by 1 and themselves). Every number can be expressed as a product of its prime factors. For example, 12 = 2 × 2 × 3 = 2² × 3.
Prime factorization is expressing a number as a product of prime numbers. For example, 60 = 2² × 3 × 5. This is useful for finding GCF, LCM, and simplifying fractions.
To find factors: 1) Start from 1 and check each number up to the square root. 2) If a number divides evenly, both it and the quotient are factors. For 36: 1×36, 2×18, 3×12, 4×9, 6×6 gives factors 1,2,3,4,6,9,12,18,36.
A perfect number equals the sum of its proper factors (factors excluding itself). The first few perfect numbers are 6 (1+2+3), 28 (1+2+4+7+14), and 496. Perfect numbers are rare and fascinating.

Last updated: 2025-01-15