A composite number
100 has 9 divisors (1, 2, 4, 5, 10, 20, 25, 50, 100) and factors as 2² × 5².
Factor calculator
Result
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How it works
Testing every integer from 1 up to the square root of the number is enough to find every divisor: for each one that divides evenly, both it and the number divided by it are divisors, which is why divisors naturally come in pairs (except for a perfect square, where the middle pair is a number paired with itself).
The prime factorization repeatedly divides out the smallest possible prime until only 1 remains — every composite number breaks down into primes in exactly one way, which is why it is called the fundamental theorem of arithmetic.
Formulas used
Divisor test
d divides n evenly if n mod d = 0, tested for d from 1 to √n
Worked examples
A prime number
17 has exactly 2 divisors (1 and 17) — the definition of a prime number.
Assumptions and limits
- Only positive integers are supported.
- For very large numbers, computing all divisors can take a moment since it tests every candidate up to the square root.
Frequently asked questions
Why does a perfect square have an odd number of divisors?
Because one divisor pairs with itself (like 10 × 10 = 100), instead of pairing with a different number — every other number has divisors that pair up into two-number groups, giving an even total.
What are the divisors of 1?
Just 1 itself. It has no prime factors and is neither prime nor composite by definition.
How can I tell if a large number is prime quickly?
You only need to test divisors up to its square root — if none divide evenly by then, no larger divisor pairs with a smaller one you have not already tried, so the number is prime.
What is a factor pair used for?
Factor pairs are the starting point for factoring quadratic expressions, and for finding the dimensions of a rectangle with a given whole-number area.
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