Factor Calculator
Enter a positive whole number to see all of its factors, factor pairs, prime factorization, and whether it is prime.
Integer Factorization & Divisor Explorer
Factors & Number Properties
What are factors?
A factor of a number n is any whole number that divides n exactly, leaving no remainder. The number 12 has six factors: 1, 2, 3, 4, 6 and 12. Every factor can be paired with another so that the pair multiplies back to 12, like 3 × 4.
The prime factorization breaks a number into its prime building blocks. For example 120 = 2 × 2 × 2 × 3 × 5, often written 2³ × 3 × 5. Every whole number greater than 1 has a unique prime factorization, a result called the Fundamental Theorem of Arithmetic.
Why factoring matters
Factoring is the foundation of simplifying fractions, finding square roots, solving quadratic equations and working with ratios. Knowing a number's factors tells you instantly what it divides by.
The calculator also reports the count and sum of the factors, and whether the number is prime (exactly two factors) or a perfect square (an odd count of factors, because the square root pairs with itself).
How to use this calculator
- Enter a positive whole number.
- Press Find factors.
- Read the full factor list and factor pairs.
- Check the prime factorization, factor count, sum and prime/perfect-square flags.
Pro tips
- A prime number has exactly two factors: 1 and itself.
- Perfect squares always have an odd number of factors.
- The sum of factors of 1 is 1; all other numbers' factor sums include at least 1 + n.
Advantages & considerations
✅ Advantages
- Lists factors, pairs and prime factorization
- Reports count, sum, prime and square flags
- Handles large numbers up to 9 quadrillion
⚠️ Considerations
- Only accepts whole numbers
- Very large primes take longer to verify