Prime Factorization
Prime Factorization Calculator
"Prime Factorization" Calculator
How to Find the Prime Factorization of a Number
How to factor 24 into primes
| 24 | 2 |
| 12 | 2 |
| 6 | 2 |
| 3 | 3 |
| 1 |
24 = 23 × 3
Left: what is left; right: the smallest prime that divides it; 1 at the bottom.
Second way — factor tree
Rule: divide by the smallest prime that divides the number evenly (2, 3, 5, 7, …) until 1 is left; the divisors to the right of the line are the answer.
See Also
- Factors of a Number - List all Factors and Factor Pairs of a Number
- Prime Number Checker - Find out whether a given number is Prime or not
- Prime Numbers List - List of all Prime Numbers - how many Prime numbers are between
FAQ
What is prime factorization?
It is writing a number as a product of prime numbers only. For 24 the factorization is 2 × 2 × 2 × 3, which is usually written as 2³ × 3.
Can a number have two different prime factorizations?
No. The fundamental theorem of arithmetic says that every integer greater than 1 breaks down into primes in exactly one way, apart from the order of the factors.
How do you factor a number by hand?
Divide by the smallest prime that fits, again and again: 1,260 ÷ 2 = 630, ÷ 2 = 315, ÷ 3 = 105, ÷ 3 = 35, ÷ 5 = 7, and 7 is already prime, so 1,260 = 2² × 3² × 5 × 7. You can stop testing divisors once the square of the divisor exceeds what is left.