Number of Factors Calculator

Enter any whole number to count its factors from the prime factorization, with the full list shown.

Examples:36483601,001

360 has 24 factors.

Prime factorization

360 = 23325

Add 1 to each exponent and multiply

(3 + 1) × (2 + 1) × (1 + 1) = 4 × 3 × 2 = 24

360 is not a perfect square, so its factors come in pairs.

The 24 factors

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

How Many Factors Does a Number Have?

You do not have to list every factor to count them. Write the number as a product of primes, add 1 to each exponent, and multiply. That one short calculation gives the number of factors.

How to Use This Number of Factors Calculator

  1. Type any whole number into the box.
  2. Press Calculate to see the count, the formula and the full list of factors.

How to Count the Factors

  1. Find the prime factorization, such as 360 = 2³ × 3² × 5.
  2. Add 1 to every exponent: (3 + 1), (2 + 1), (1 + 1).
  3. Multiply: 4 × 3 × 2 = 24 factors.
Handwritten notebook page counting the factors of 360 from 2 cubed times 3 squared times 5 to get 24
360 = 2³ × 3² × 5, so (3 + 1) × (2 + 1) × (1 + 1) = 24 factors.

Why Adding 1 Works

A factor can use a prime zero times, once, or up to its full exponent. A prime with exponent 3 has 4 choices: 0, 1, 2 or 3 copies. The choices for different primes are independent, so you multiply them.

Perfect Squares Have an Odd Count

Factors normally come in pairs. In a perfect square like 36, the middle factor 6 pairs with itself, so 36 has 9 factors, an odd number.

Handwritten notebook page counting the nine factors of 36 from 2 squared times 3 squared
36 = 2² × 3², so (2 + 1) × (2 + 1) = 9 factors.

Worked Examples

Common mistakes

Number of Factors Calculator FAQs

How do you find the number of factors of a number?

Write the number as a product of primes. Add 1 to each exponent, then multiply the results. For 360 = 2³ × 3² × 5 you get 4 × 3 × 2 = 24.

How many factors does 36 have?

36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18 and 36. Since 36 = 2² × 3², the count is (2 + 1) × (2 + 1) = 9.

Why do you add 1 to each exponent?

Each prime can be used 0 times, 1 time, up to its full exponent. A prime with exponent 3 has 4 choices, and the choices for different primes multiply.

Which numbers have an odd number of factors?

Only perfect squares. Factors normally come in pairs, but for a square the middle factor pairs with itself, so the count is odd.

How many factors does a prime number have?

Exactly 2: 1 and the prime itself. A prime p equals p¹, so the count is (1 + 1) = 2.

How many factors does 1 have?

Just one, which is 1 itself. It is the only number with a single factor.

How many factors does 1001 have?

8 factors. 1001 = 7 × 11 × 13, so the count is 2 × 2 × 2 = 8.

Does the count include 1 and the number itself?

Yes. Every number is divisible by 1 and by itself, and both are counted as factors.

More Worked Examples

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