How to Find Factors of a Number
Published 2026-11-03
Factor calculator searches mean “what divides this integer,” not factorial. If d divides n, so does n/d. Walking d from 1 to √n collects the whole list. Prime factorization then writes n as a product of primes.
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Run these formulas with your own numbers. Math stays in your browser.
Open Factor Calculator →Our factor calculator does both for one positive integer. 84 = 2² × 3 × 7 with 12 factors. It does not take a list of numbers (use GCF/LCM) and it does not compute n! (scientific calculator, n ≤ 170).
Open the factor calculator
Enter a whole number. The default 84 should show factorization 2^2 × 3 × 7 and twelve factors. Prime? is yes only when the factorization is a single prime.
Pair divisors through the square root
For 84, √84 ≈ 9.2. Test 1–9: 1×84, 2×42, 3×28, 4×21, 6×14, 7×12. Sort: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
If d | n and d ≤ √n, both d and n/d are factors
n = p₁^a₁ × p₂^a₂ × …
Count factors from exponents
If n = p^a × q^b × …, the factor count is (a+1)(b+1)…. For 84, (2+1)(1+1)(1+1) = 12.
| n | Prime factorization | Factor count |
|---|---|---|
| 1 | 1 | 1 |
| 13 | 13 | 2 |
| 36 | 2^2 × 3^2 | 9 |
| 84 | 2^2 × 3 × 7 | 12 |
| 97 | 97 | 2 |
Squares, primes and 1
Squares have an odd number of factors because the square root is counted once. Primes have exactly two. 1 has one factor and is not prime — the prime number checker agrees.
- List divisor pairs through √n.
- Divide out smallest primes for the factorization.
- Use GCF/LCM tools if the question has two or more numbers.
From one factorization to GCF and LCM
Factor 12 = 2² × 3 and 18 = 2 × 3² on this tool, then read GCF and LCM off the exponents: lowest powers 2¹ × 3¹ = 6, highest powers 2² × 3² = 36. Confirm on the GCF and LCM calculators. That is why a “factor calculator” page still belongs next to those two searches. Perfect squares show an odd factor count because the square root is a repeated divisor listed once — 36 has nine factors, 84 has twelve. Factorial 84! is a different number entirely; the scientific calculator will refuse it because 84! is far past 170!. Use this page for divisors of one integer, not for a list of several integers at once.
Use the free tool
Run these formulas with your own numbers. Math stays in your browser.
Open Factor Calculator →Frequently Asked Questions
Is this factorial?
No. n! is the scientific calculator.
Are negative factors listed?
No. Positive divisors only.
What about 1?
One factor: 1. Not prime.
Can I enter a decimal?
No.
Does the count include n itself?
Yes. 1 and n are always factors of n ≥ 1.
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