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Factor Calculator

Find all the factors of a number, its factor pairs, how many factors it has and their sum, and whether the number is prime.

Results

ItemValue

Steps

StepWorking
Works for whole numbers from 1 to 1,000,000,000,000. Negative numbers have the same factors with a minus sign.

Quick Answer

A factor is a whole number that divides another number with no remainder. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36, so 36 has 9 factors. To find them, test each number up to the square root of 36 and pair it with its partner, such as 4 × 9.

Last updated: 2 November 2026 ·How we calculate this: trial division up to the square root

Table of Contents

How This Factor Calculator Works

Enter a whole number. The calculator tests every whole number from 1 up to its square root. Each number that divides evenly is a factor, and so is its partner. It lists all the factors in order, the factor pairs, how many there are, their sum, and whether the number is prime.

Quick explanation: factors come in pairs that multiply to the number.

  • Prime: exactly two factors, 1 and itself.
  • Composite: more than two factors.
  • Square numbers: have an odd number of factors.

How to Use the Factor Calculator

  1. Enter a whole number.
  2. Press Calculate.
  3. Read the list of factors and the factor pairs.
  4. See whether the number is prime or composite.
  5. Use the steps to follow the method by hand.

Core Rules

  • Factor: a divides n if n ÷ a has no remainder
  • Pairs: if a is a factor, so is n ÷ a
  • Stop at √n: every pair has one factor at or below √n
  • Proper factors: all factors except the number itself

Key Terms

  • Factor: a whole number that divides another with no remainder.
  • Factor pair: two factors that multiply to the number.
  • Prime number: a number with exactly two factors.
  • Composite number: a number with more than two factors.
  • Perfect number: a number equal to the sum of its proper factors, such as 6 or 28.

Worked Example

Find the factors of 120.

  • √120 ≈ 10.95, so test 1 to 10
  • Pairs: 1 × 120, 2 × 60, 3 × 40, 4 × 30, 5 × 24, 6 × 20, 8 × 15, 10 × 12
  • Factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 (16 factors)

Real-Life Examples

  • Arranging rows: 24 chairs can be set in rows of 1, 2, 3, 4, 6, 8, 12, 24.
  • Simplifying fractions: common factors of 36 and 48 help reduce 36/48 to 3/4.
  • Even teams: 30 students can split into equal groups of 2, 3, 5, 6, 10, 15.
  • Checking primes: 97 has only 2 factors, so it is prime.

Factors vs Multiples vs Prime Factors

  • Factors: numbers that divide into it. Factors of 12: 1, 2, 3, 4, 6, 12.
  • Multiples: numbers it divides into. Multiples of 12: 12, 24, 36 and so on.
  • Prime factors: the primes that multiply to make it: 12 = 2 × 2 × 3. Try our Prime Factorization Calculator.

Factors of Common Numbers

NumberFactorsCount
121, 2, 3, 4, 6, 126
161, 2, 4, 8, 165
181, 2, 3, 6, 9, 186
241, 2, 3, 4, 6, 8, 12, 248
301, 2, 3, 5, 6, 10, 15, 308
361, 2, 3, 4, 6, 9, 12, 18, 369
481, 2, 3, 4, 6, 8, 12, 16, 24, 4810
601, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 6012
721, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 7212
1001, 2, 4, 5, 10, 20, 25, 50, 1009

Divisibility Shortcuts

  • 2: the last digit is even.
  • 3: the digits add up to a multiple of 3.
  • 5: the last digit is 0 or 5.
  • 9: the digits add up to a multiple of 9.
  • 10: the last digit is 0.

Common Mistakes to Avoid

  • Forgetting 1 and the number itself. Both are always factors.
  • Stopping too early. Test up to the square root, then use the pairs.
  • Counting a square root twice. In 6 × 6 = 36, 6 is one factor.
  • Mixing factors and multiples. Factors are smaller or equal; multiples are larger or equal.
  • Calling 1 prime. 1 is neither prime nor composite.

Frequently Asked Questions

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

1, 2, 3, 4, 6, 9, 12, 18, 36.

1, 2, 4, 5, 10, 20, 25, 50, 100.

Test each whole number from 1 to the square root. When one divides evenly, write it and its partner.

Yes. 1 divides every whole number.

One factor pairs with itself, like 6 × 6 = 36, so it is counted once.

A number greater than 1 with exactly two factors: 1 and itself.

No. You cannot divide by 0.

One whose proper factors add up to itself. 6 = 1 + 2 + 3.

Yes, the same factors with minus signs, such as −2 × −6 = 12.

Factors are all the divisors. Prime factors are only the primes that multiply to make the number.

Up to 1,000,000,000,000.

References & Sources

SourceUsed ForLink
Wikipedia, Divisor Factors, divisors and their properties. https://en.wikipedia.org/wiki/Divisor
Wikipedia, Perfect number Perfect, abundant and deficient numbers. https://en.wikipedia.org/wiki/Perfect_number