Factor Calculator
Factors & Factor Pairs Tool
Understanding Factors
Every whole number can be broken down into the smaller numbers that divide into it evenly — its factors. Finding them is the starting point for simplifying fractions, finding common denominators, and understanding prime numbers.
Factors always come in pairs that multiply together to give the original number — find one half of a pair, and you automatically know the other half.
A number with exactly two factors (1 and itself) is prime. Any number with more than two factors is composite — the factor count is the quickest way to tell them apart.
Worked Example
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, made up of the factor pairs 1 × 24, 2 × 12, 3 × 8, and 4 × 6. Since 24 has eight factors (more than two), it's a composite number.
Key Takeaways
- 1 and the number itself are always factors of any positive whole number.
- A perfect square has one factor that pairs with itself, such as 5 × 5 = 25, giving it an odd total number of factors.
- Checking divisibility only up to the square root of n is enough to find every factor, since factors above that point are just the mirror image of factors below it.
Frequently Asked Questions
- Enter any positive whole number.
- Click "Calculate."
- See every factor of that number listed in order, along with its factor pairs and whether the number is prime or composite.
A factor (or divisor) of a number is any whole number that divides into it with no remainder. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, because each one divides 24 evenly.
A factor pair is two factors that multiply together to give the original number. For 24, the factor pairs are 1 × 24, 2 × 12, 3 × 8, and 4 × 6 — every factor pair uses up exactly two entries from the full factor list.
A number is prime if it has exactly two factors: 1 and itself. If it has more than two factors, it's composite. The number 1 is neither prime nor composite, since it only has one factor (itself).
Instead of checking every number up to n, the calculator only checks divisors up to the square root of n. Whenever it finds a divisor i, it automatically also records the paired divisor n ÷ i, since factors always come in matching pairs (except for the middle factor of a perfect square, which pairs with itself).
Factors are only defined for positive whole numbers, so the calculator shows a clear error if the entry is zero, negative, or not a whole number.