Factor Calculator
Find every factor (divisor) of a positive whole number.
| Factor Pair | Product |
|---|---|
| 1 × 60 | 60 |
| 2 × 30 | 60 |
| 3 × 20 | 60 |
| 4 × 15 | 60 |
| 5 × 12 | 60 |
| 6 × 10 | 60 |
Every row multiplies out to 60 — pairing the smallest factor with the largest and working inward is the fastest way to find them all.
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About the Factor Calculator
A factor of a number is any whole number that divides into it evenly, with nothing left over. Every whole number greater than 1 has at least two factors — 1 and itself — and most have several more tucked in between, arranged neatly in pairs that multiply back to the original number.
This comes up constantly in school math: simplifying fractions to lowest terms, factoring expressions in algebra, or splitting a group of items into equal-sized batches. It's also just a handy everyday tool — figuring out every way to arrange a fixed number of items into equal rows and columns, for example, is really a factor question in disguise.
Larger numbers tend to have more factors, but not predictably — a number like 60 has twelve factors thanks to its rich mix of small prime building blocks, while a number like 61 (prime) has only two: 1 and 61 itself.
How it’s calculated
Finding every factor of a number means testing which whole numbers divide into it with no remainder. Checking divisors only up to the square root of the number is enough — every factor above that square root is guaranteed to be paired with one already found below it, since factors always come in pairs that multiply to the original number.
That's why factors are naturally listed as pairs: for 60, the pair (4, 15) multiplies back to 60, and so does (5, 12), (6, 10), (1, 60), (2, 30), and (3, 20) — six pairs, twelve factors total.
Frequently asked questions
What is a factor of a number?
A factor is any whole number that divides evenly into another number with no remainder. For example, 6 is a factor of 24 because 24 ÷ 6 = 4 exactly, with nothing left over.
What's the difference between factors and multiples?
Factors divide into a number (the factors of 12 are smaller than or equal to 12: 1, 2, 3, 4, 6, 12). Multiples are what you get multiplying a number up (the multiples of 12 go the other direction: 12, 24, 36, 48…) — factors and multiples are essentially inverses of each other.
How many factors does a number have?
It depends entirely on the number's prime building blocks — a number with many small prime factors tends to have far more total factors than a prime number of similar size, which only ever has exactly two: 1 and itself.
What's the difference between this and the prime factorization calculator?
This lists every whole-number divisor of a number. Prime factorization breaks the number down into only its prime building blocks (with exponents) — a more compact, unique representation that this calculator's full factor list is actually built from.
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