Free factor calculator
Find all factors of any positive integer — enter a number to see every integer that divides it evenly, updated live, as you type.
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All positive divisors of n found by trial division up to √n.
Results are estimates. Consult a professional.
How the factor calculator works
A factor of a whole number n is any positive integer that divides n evenly (with no remainder). The calculator uses trial division: it tests every integer from 1 up to √n. When i divides n, both i and n/i are added to the factor list — so each step potentially finds two factors at once, making the algorithm efficient.
Worked example: factors of 36 and 48
Trial division up to √36 = 6 and √48 ≈ 6.93 (test up to 6) finds all factor pairs efficiently.
Factors of numbers 12 to 60
The table shows a selection of common numbers with their complete factor lists and total factor count. Highly composite numbers like 24, 36, and 60 have unusually many factors.
| Number | Factors | Count |
|---|---|---|
| 12 | 1, 2, 3, 4, 6, 12 | 6 |
| 18 | 1, 2, 3, 6, 9, 18 | 6 |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 | 8 |
| 30 | 1, 2, 3, 5, 6, 10, 15, 30 | 8 |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | 9 |
| 48 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 | 10 |
| 60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | 12 |
Source: trial division; all factor lists are complete and in ascending order
Tips for finding factors
Factoring is a building block for simplifying fractions, finding GCD/LCM, and solving algebra problems. These habits make the process faster and less error-prone.
- Only test up to √n — every factor above √n has a corresponding partner below √n. Testing beyond √n wastes time and adds nothing new to the list.
- Divisibility shortcuts — a number is divisible by 2 if it's even; by 3 if its digit sum is divisible by 3; by 5 if it ends in 0 or 5. These quick checks eliminate candidates before full division.
- Prime numbers have exactly two factors — 1 and themselves. If you find only 1 and n after testing all integers up to √n, the number is prime.
- Perfect squares have an odd factor count — because the square root pairs with itself rather than a distinct partner. Use this to double-check: if your factor count is odd, verify that n is a perfect square.
- Factor count from prime factorisation — if n = p₁^a × p₂^b × …, the total number of factors is (a+1)(b+1)…. For 36 = 2² × 3²: (2+1)(2+1) = 9 factors ✓.
Accuracy and limitations
The trial-division algorithm is mathematically exact for all positive integers within JavaScript's safe integer range (up to 2⁵³ − 1 ≈ 9 × 10¹⁵). For very large inputs (above ~10⁸), the calculation may take a moment as the algorithm tests up to √n candidates. The calculator only finds positive integer factors; it does not return negative factors or fractional divisors, which are sometimes included in more advanced algebraic contexts. The input must be a positive integer — decimals and negative numbers are not factored.
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About this calculator
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