Factor Calculator: Simple, Fast, and Fun

Enter a number to find all its factors and prime factorization:

How Factors Are Found

The tool checks every integer from 1 up to the number itself, keeping any that divide evenly (remainder zero). For the factor pairs list, it only needs to check up to the square root of the number, since factors always come in pairs that multiply back to the original value.

Worked Example: 36

All factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 (9 factors total). Factor pairs: 1x36, 2x18, 3x12, 4x9, 6x6. Since 36 has more than two factors, it's composite, not prime. Prime factorization: divide repeatedly by the smallest prime that fits - 36/2=18, 18/2=9, 9/3=3, 3/3=1 - giving 2 squared x 3 squared.

Prime vs. Composite

The tool flags a number as prime only when it has exactly two factors: 1 and itself. A number like 37 would show "All Factors: 1, 37" and be labeled prime, with no further prime factorization needed since it can't be broken down further.

Input Limits

Only positive whole numbers are accepted; the field defaults to 12 on page load. Because the factor search is a simple loop up to n, very large numbers (in the millions) will take noticeably longer to process in the browser than small ones.