ToolBark
Math

Factors of a Number Calculator

Find every divisor of any number — and know if it's prime

Input

Enter any whole number from 1 to 1,000,000,000.

Try an example

Classification

Composite NumberAbundant number

36 is composite — it has 9 divisors including 1 and itself.

All Factors of 369

123469121836

Highlighted in red: 1 and 36 (trivial divisors)

Prime Factorization

36=22×32
2 appears2 times
3 appears2 times

Stats

Number of divisors (τ)9
Sum of all divisors (σ)91
Proper divisors (excluding itself)1, 2, 3, 4, 6, 9, 12, 18
Sum of proper divisors55
Abundance (σ − 2n)19

How It Works

A factor (or divisor) of n is any integer that divides n with no remainder. This tool finds all factors by trial division up to √n, then tests primality, builds the full prime factorization, and computes divisor sums.

12

Factors: 1, 2, 3, 4, 6, 12

17

Prime — only 1 and 17

28

Perfect: proper divisor sum = 28

About

The Factors of a Number Calculator instantly lists every factor (divisor) of any positive integer, shows the complete prime factorization with exponents, and determines whether the number is prime, composite, perfect, abundant, or deficient. Whether you are checking homework, studying number theory, or simplifying fractions, this free tool gives you a full divisor breakdown in one click.

FAQ
What is a factor of a number?+

A factor (or divisor) of a whole number n is any positive integer that divides n exactly, leaving no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

How do I know if a number is prime?+

A prime number has exactly two factors: 1 and itself. If this calculator shows only those two divisors, the number is prime. Examples include 2, 3, 5, 7, 11, and 97.

What is a perfect number?+

A perfect number equals the sum of all its proper divisors (divisors excluding itself). The classic example is 28: its proper divisors are 1, 2, 4, 7, and 14, which sum to 28.

What is prime factorization and why does it matter?+

Prime factorization expresses a number as a product of prime numbers raised to their respective powers (e.g., 360 = 2³ × 3² × 5). It is fundamental to finding GCDs, LCMs, simplifying fractions, and solving problems in cryptography.

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