Factor Calculator

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Factor Calculator

Discover all positive factors of any integer. Identify prime numbers, count divisors, and analyze the complete factor set with instant calculations.

Last updated: May 2026 | By Patchworkr Team

Enter an integer to analyze
Total Factors
16
Is Prime?
NO
Sum
360
12345681012152024304060120

Factor Examples

NumberCountPrime?All Factors
126NO1, 2, 3, 4, 6, 12
172YES1, 17
6012NO1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
1009NO1, 2, 4, 5, 10, 20, 25, 50, 100
11NO1

What are Factors?

Factors (or divisors) are integers that divide evenly into a given number with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each divides 12 exactly. Finding all factors of a number is a fundamental operation in number theory with applications spanning from simplifying fractions to cryptography.

Key concepts:

  • Every positive integer is divisible by 1 and itself
  • If a × b = n, then both a and b are factors of n
  • Factors come in pairs: if a is a factor, so is n ÷ a
  • A number is prime if it has exactly 2 factors: 1 and itself
  • To find all factors, test divisors up to √n

How to Use This Calculator

  1. Enter a positive integer in the input field. Any whole number from 1 onwards works.
  2. View results instantly. The calculator uses trial division up to √n to efficiently find all factors and determine primality.
  3. Interpret the output: "Total Factors" shows how many divisors the number has. "Is Prime?" indicates whether the number is prime (2 factors: 1 and itself).
  4. Use the factor list to understand the number's structure. The sum of factors is useful for perfect number detection and other number-theoretic functions.
  5. Apply factors in practice: Simplify fractions, find common denominators, or compute GCD/LCM for further calculations.

Example: Factor 360

Problem:
Find all positive factors of 360 and determine if it is prime.
Solution:
Test divisors from 1 to √360 ≈ 18.97. For each divisor found, record both the divisor and its complement (360 ÷ divisor).
Divisor Pairs:
(1, 360), (2, 180), (3, 120), (4, 90), (5, 72), (6, 60), (8, 45), (9, 40), (10, 36), (12, 30), (15, 24), (18, 20)
Answer:
All Factors (24 total):
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Prime? NO (more than 2 factors)

Frequently Asked Questions

What's the difference between factors and prime factors?

Factors are all divisors of a number. Prime factors are only the prime numbers that divide it. For 360, factors include 2, 4, 6, etc., but prime factors are just 2, 3, and 5.

Why is 1 considered a factor?

Because 1 divides evenly into every positive integer: $n ÷ 1 = n$ with no remainder. By definition, 1 is always a factor.

Is zero a factor of anything?

No. Division by zero is undefined, and zero divided by anything (except zero) is zero, not an integer. We only consider positive factors here.

What's a perfect number?

A perfect number equals the sum of its proper factors (all factors except itself). For example, 6 = 1 + 2 + 3. The next is 28 = 1 + 2 + 4 + 7 + 14.

How do I use factors to simplify fractions?

Find the GCD (greatest common divisor) of numerator and denominator using their factors. Then divide both by the GCD. For 12/18, GCD is 6, so 12/18 = 2/3.

Why factor 12 but not 13?

13 is prime—it has only two factors: 1 and 13. 12 is composite and has six factors: 1, 2, 3, 4, 6, 12. The calculator handles both the same way.

What's trial division?

Trial division tests whether each integer from 2 to √n divides n evenly. If yes, it's a factor; if no remainder is found for any divisor up to √n, the number is prime.

How are factors used in real life?

Factors help simplify recipes (dividing ingredients), split groups evenly, compute schedules, and solve modular arithmetic problems in cryptography and computer science.

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