Factors Calculator

About the Factors Calculator

A factor (or divisor) of an integer n is any whole number that divides n evenly leaving a remainder of zero. Every integer greater than 1 has at least two factors: 1 and itself.

Our Factors Calculator finds all positive factors of any number, counts the total number of divisors, computes the sum of factors, and identifies whether the number is a Prime Number or a Composite Number.

Factor Pair & Divisor Formulas

Factors always come in pairs that multiply to the original number n:

How to Find All Factors of a Number

1. Start with 1 and the Number Itself: 1 and n are always the first factor pair.
2. Test Integers Up to √n: Divide n by each integer 2, 3, 4, ... up to the square root of n.
3. Record Both Numbers in Each Pair: Whenever n ÷ a leaves no remainder, both a and n ÷ a are factors of n.

Worked Example: To find the factors of 36, test up to √36 = 6: pairs are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6). Sorted factors: 1, 2, 3, 4, 6, 9, 12, 18, 36 (9 factors total).

Frequently Asked Questions (FAQ)

Why do some numbers have an odd number of factors?

Only perfect squares (like 4, 9, 16, 25, 36) have an odd number of factors, because their square root pairs with itself (e.g., 6 × 6 = 36).

What is the difference between factors and multiples?

Factors divide a number evenly and are less than or equal to the number (factors of 10 are 1, 2, 5, 10). Multiples are obtained by multiplying the number by integers and are greater than or equal to it (10, 20, 30, 40…).