Prime Factorization Calculator
This prime factorization calculator breaks any whole number down into the primes that multiply to make it. Type a number and you'll get the factorization in exponent form, a factor tree that shows each split, the full list of divisors, and a check of whether the number's prime. It's the fast way to see what a number is really built from.
- Exponent form
- Factor tree
- All divisors listed
- Prime or composite
- Steps shown
Last updated June 16, 2026 Divide by primes until you reach 1 Reviewed by the Calcowa math team
Enter a whole number of 2 or more. Very large numbers may take a moment.
Enter a whole number of 2 or more.
What is prime factorization?
Prime factorization is writing a number as a product of prime numbers, the building blocks that can't be broken down any further. Every whole number above 1 has exactly one prime factorization, a fact known as the fundamental theorem of arithmetic. So 360 is always 2³ × 3² × 5, no matter how you split it along the way. Those primes are what the number is genuinely made of, and it's the most basic description of a number there is.
How do you find the prime factorization?
The method is repeated division by primes. Here's how the calculator factors 360:
- 1
Divide by the smallest prime360 ÷ 2 = 180. Two goes in, so 2 is your first prime factor.
- 2
Keep dividing by 2180 ÷ 2 = 90, then 90 ÷ 2 = 45. Two won't divide 45, so move up.
- 3
Move to the next prime45 ÷ 3 = 15, then 15 ÷ 3 = 5. Now you're down to a prime.
- 4
Collect the primesYou divided by 2, 2, 2, 3, 3, and stopped at 5, so 360 = 2³ × 3² × 5.
Reading the factor tree
The factor tree above shows each division as a branch. At every step the smallest prime breaks off to one side while the rest carries on down, until the final number is prime. The primes that drop off, plus that last one, are the whole factorization. The neat part is that you'd reach the same primes splitting in any order, so there isn't a wrong path through the tree, only a tidy one.
What are the prime factors versus all factors?
A factor is any number that divides evenly, while a prime factor is one that's also prime. The number 360 has 24 factors in total, from 1 up to 360, but only three distinct prime factors: 2, 3, and 5. The result above lists every divisor alongside the prime factorization, so you'll see both at once. Knowing the prime factors makes the rest easy, since multiplying combinations of them produces every factor on the list, so you don't miss any. To use those primes for two numbers at once, the GCF and LCM calculator takes it from here.
Frequently asked questions
What is the prime factorization of 36?
The prime factorization of 36 is 2² × 3², which is 2 × 2 × 3 × 3. Divide 36 by 2 to get 18, by 2 again to get 9, then by 3 twice to reach 1. That gives two 2s and two 3s.
Divide by the smallest prime that fits, then keep dividing the result until you're left with 1. For 360, you divide by 2 three times to reach 45, then by 3 twice to reach 5, which is prime. Collecting those primes gives 2 × 2 × 2 × 3 × 3 × 5, written 2³ × 3² × 5. This prime factorization calculator runs that division for you and draws the factor tree.
The prime factorization of 360 is 2³ × 3² × 5, which is 2 × 2 × 2 × 3 × 3 × 5. You get there by dividing by 2 until it won't divide evenly, then by 3, leaving 5. Multiply those primes back together and you'll return to 360, which is the quick check that the factorization is right.
No, 1 isn't a prime number. A prime has exactly two distinct factors, itself and 1, and 1 only has one factor, so it doesn't qualify. It isn't composite either; it's a special case that sits outside both groups. That's why the prime factorization of 1 is empty: there aren't any primes to list.
A factor is any whole number that divides evenly into your number, while a prime factor is a factor that's also prime. The number 12 has factors 1, 2, 3, 4, 6, and 12, but its prime factors are only 2 and 3. The calculator lists both: the full set of divisors and the prime factorization.
A factor tree is a diagram that splits a number into two factors, then keeps splitting each branch until every end is a prime. It's a visual way to reach the prime factorization, and the order you split in doesn't change the final primes. The tool draws one above, breaking off the smallest prime at each step.
Once you have the prime factorization of two numbers, the greatest common factor multiplies the primes they share at the lowest power, and the least common multiple multiplies every prime at the highest power. So prime factors are the engine behind both. The GCF and LCM calculator uses exactly this method.
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