Factor Calculator

Find all factors, prime factorization, factor pairs, and test divisibility rules

Calculate Factors

Enter any positive integer up to 1,000,000

Common Factor Examples

Factors of 12:

1, 2, 3, 4, 6, 12

6 factors total

Factors of 24:

1, 2, 3, 4, 6, 8, 12, 24

8 factors total

Factors of 17:

1, 17

Prime number - 2 factors

Factor Tips

Every number has at least two factors: 1 and itself

Prime numbers have exactly two factors

Factors come in pairs that multiply to give the original number

Perfect squares have an odd number of factors

Understanding Factors and Factorization

What is a Factor?

A factor is a number that divides evenly into another number with no remainder. Factors are fundamental in mathematics and help us understand the structure of numbers.

Types of Factorization:

  • All Factors: Every number that divides the input evenly
  • Prime Factorization: Breaking down into prime number components
  • Factor Pairs: Numbers that multiply together to give the original

Mathematical Applications

Simplifying Fractions

Find common factors to reduce fractions to lowest terms

Finding GCD and LCM

Use prime factorization to find greatest common divisor and least common multiple

Solving Equations

Factor polynomials and solve quadratic equations

Cryptography

RSA encryption relies on difficulty of factoring large numbers

Key Divisibility Rules

Rule of 2

A number is divisible by 2 if it's even (ends in 0, 2, 4, 6, or 8)

Rule of 3

A number is divisible by 3 if the sum of its digits is divisible by 3

Rule of 5

A number is divisible by 5 if it ends in 0 or 5

Rule of 9

A number is divisible by 9 if the sum of its digits is divisible by 9

Rule of 4

A number is divisible by 4 if its last two digits form a number divisible by 4

Rule of 8

A number is divisible by 8 if its last three digits form a number divisible by 8