# Factor Calculator

Find every factor of a positive integer instantly. Shows factor pairs, count, sum, and primality. Works for numbers up to 1,000,000.

## What this calculates

Enter any positive integer and get all of its factors in one click. The calculator lists every factor, shows factor pairs, counts them, adds them up, and tells you whether the number is prime. Try 60 and you will see 12 factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

## Inputs

- **Number** — min 1 — A positive whole number to find factors of.

## Outputs

- **All Factors** — formatted as text — Every factor of the number, listed in order.
- **Factor Pairs** — formatted as text — Pairs of numbers that multiply to give the original number.
- **Number of Factors** — How many factors the number has.
- **Sum of Factors** — The total when all factors are added together.
- **Is Prime?** — formatted as text — Whether the number has exactly two factors (1 and itself).

## Details

**What Is a Factor?**

A factor of a number is any integer that divides it evenly (with no remainder). For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

**Finding Factors**

Start at 1 and test each integer up to the square root of the number. Each time you find a factor, its pair (the number divided by that factor) is also a factor. For 36: testing 1 through 6 gives pairs (1, 36), (2, 18), (3, 12), (4, 9), (6, 6).

**Factor Pairs**

Factor pairs are two numbers that multiply together to produce the original number. The number 24 has factor pairs: (1, 24), (2, 12), (3, 8), (4, 6).

**Prime Numbers**

A prime number has exactly two factors: 1 and itself. Numbers like 2, 3, 5, 7, 11, and 13 are prime. The number 1 is a special case and is considered neither prime nor composite.

**Sum of Factors**

The sum of all factors (also called the sigma function) has uses in number theory. If the sum of a number's proper factors (all factors except itself) equals the number, it is called a perfect number. For example, 6 = 1 + 2 + 3.

## Frequently Asked Questions

**Q: What are the factors of 100?**

A: The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, and 100. That is 9 factors total, with factor pairs (1, 100), (2, 50), (4, 25), (5, 20), and (10, 10).

**Q: How is factoring different from prime factorization?**

A: Factoring lists all divisors of a number (e.g., factors of 12 are 1, 2, 3, 4, 6, 12). Prime factorization breaks a number into a product of only prime numbers (e.g., 12 = 2 x 2 x 3). Both are useful but answer different questions.

**Q: Is 1 a prime number?**

A: No. By mathematical convention, 1 is neither prime nor composite. A prime number must have exactly two distinct factors: 1 and itself. Since 1 has only one factor (itself), it does not qualify.

**Q: What is a perfect number?**

A: A perfect number equals the sum of its proper factors (all factors except itself). The first few perfect numbers are 6 (1+2+3), 28 (1+2+4+7+14), and 496. They are extremely rare.

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Source: https://vastcalc.com/calculators/math/factor
Category: Math
Last updated: 2026-04-08