How to Find All Factors of a Number
Factors are the building blocks of numbers. They are the integers that can be multiplied together to get another number. Understanding factors is a key skill in mathematics, essential for everything from simplifying fractions to cryptography. I built this calculator to be a simple and powerful tool for both finding all the factors of a number and breaking it down into its unique prime factorization.
How to Use This Factor Calculator
Simply enter any positive whole number into the input field. The calculator will instantly provide you with two key pieces of information:
- Prime Factorization: The set of prime numbers that, when multiplied together, equal your original number.
- All Factors: A complete list of all integers that divide your number evenly.
What Is Prime Factorization?
Every whole number greater than 1 is either a prime number or can be written as a unique product of prime numbers. A prime number is a number that has only two factors: 1 and itself (like 2, 3, 5, 7, etc.).
My calculator finds these prime building blocks for you. For example, for the number 120, the prime factorization is:
2³ × 3 × 5
This tells you that 2 × 2 × 2 × 3 × 5 = 120.
How Does the Calculator Find All Factors?
Once we have the prime factorization, we can find all other factors. For 120, any combination of its prime factors (2, 2, 2, 3, 5) will also be a factor.
- Just the primes: 2, 3, 5
- Combinations: 2×2=4, 2×3=6, 2×5=10, 3×5=15, 2×2×2=8, 2×2×3=12, and so on.
The calculator automates this process to give you the complete list, which for 120 is 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Factors of Common Numbers
Here are the complete factor lists for some frequently searched numbers. Enter any other number in the calculator above to get its factors and prime factorization instantly.
| Number | All factors | Prime factorization |
|---|---|---|
| 12 | 1, 2, 3, 4, 6, 12 | 2² × 3 |
| 16 | 1, 2, 4, 8, 16 | 2⁴ |
| 18 | 1, 2, 3, 6, 9, 18 | 2 × 3² |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 | 2³ × 3 |
| 30 | 1, 2, 3, 5, 6, 10, 15, 30 | 2 × 3 × 5 |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | 2² × 3² |
| 48 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 | 2⁴ × 3 |
| 60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | 2² × 3 × 5 |
| 72 | 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 | 2³ × 3² |
| 100 | 1, 2, 4, 5, 10, 20, 25, 50, 100 | 2² × 5² |