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Factor Calculator

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Enter a whole number to find all of its factors.

Factor Calculator

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Factors
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Number of factors
12
Prime?
No

The method

Check every whole number from 1 up to √n If it divides evenly, both it and its pair (n / that number) are factors
Example

60: checking 1 through 7 (√60 ≈ 7.75) finds 1×60, 2×30, 3×20, 4×15, 5×12, 6×10 - giving 12 factors total: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Step-by-step guide

  1. Enter any positive whole number.
  2. Read all its factors, the total count, and whether the number is prime.

Why checking only up to the square root is enough

Factors always come in pairs that multiply to the original number, and one factor in each pair is always less than or equal to the square root while the other is greater than or equal to it - there's no way to have both factors in a pair exceed the square root, since their product would then exceed the original number. This is exactly why this calculator (and factor-finding in general) only needs to test candidate divisors up to the square root: every factor pair gets captured by checking that range alone, without needing to check all the way up to the number itself.

Common mistakes

Confusing "factors" with "prime factors" - factors include every number that divides evenly (like 4, 6, 10, 12 for 60), while prime factorization breaks a number down into only its prime building blocks (2, 2, 3, 5 for 60).
Forgetting that 1 and the number itself are always factors - even prime numbers have exactly these two factors, never zero.

Frequently asked questions

What makes a number prime?

A prime number has exactly two factors: 1 and itself. Any number with more than two factors (like 60, with twelve) is called composite.

Does this find prime factorization too?

This lists all factors, not the prime factorization specifically - but you can identify the prime factors within the list by checking which listed factors are themselves prime.

Is 1 considered prime?

No - by mathematical convention, 1 is neither prime nor composite, since it only has one factor (itself), not the two required to be considered prime.

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