Prime Factorization Calculator
Calculate your Prime factors in seconds with the free Prime Factorization Calculator. No registration needed.
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Prime factors
What is a Prime Factorization Calculator?
A prime factorization calculator breaks any whole number down into its prime factors — the prime numbers that multiply together to produce the original number. Every integer greater than 1 has exactly one set of prime factors (ignoring order). This is useful for simplifying fractions, finding the GCF or LCM of multiple numbers, understanding number properties, and solving problems in number theory and cryptography.
How to find prime factorisation manually
The most common method is trial division by primes:
Step 1: Start with the smallest prime number, 2. If the number is even, divide by 2.
Step 2: Keep dividing by 2 until the result is odd.
Step 3: Move to the next prime (3, then 5, then 7, then 11) and repeat.
Step 4: Continue until the remaining number is itself a prime.
You can also use a factor tree: write the number at the top, branch it into a pair of factors, and branch each composite factor until all branches end in primes. The primes are the prime factors of the original number.
Example calculation
Find the prime factorisation of 360.
Step 1: 360 is even. 360 ÷ 2 = 180. (factor: 2)
Step 2: 180 is even. 180 ÷ 2 = 90. (factor: 2)
Step 3: 90 is even. 90 ÷ 2 = 45. (factor: 2)
Step 4: 45 is not even. Divide by 3: 45 ÷ 3 = 15. (factor: 3)
Step 5: 15 ÷ 3 = 5. (factor: 3)
Step 6: 5 is prime. Done.
Prime factorisation of 360: 2³ × 3² × 5. In expanded form: 2 × 2 × 2 × 3 × 3 × 5.
Common mistakes
- Missing a factor — if the original number does not divide evenly and you skip primes, you may miss factors. Always check each prime in order.
- Stopping too early — if the remaining number is still composite, keep going. Do not stop just because it is no longer divisible by 2.
- Confusing factors with prime factors — a factor can be composite (e.g. 4 is a factor of 60), but a prime factor must be prime. Only list primes in a prime factorisation.
- Treating 1 as a prime factor — 1 is not a prime number. Every number technically has infinite 1s, but they are never included in prime factorisation.
Frequently asked questions
How do I find the prime factorization of a number?
Start by dividing the number by the smallest prime (2). If it divides evenly, write down 2 and divide the result. Repeat until the number no longer divides by 2, then try 3, then 5, then 7, continuing upward. When the remaining number is a prime, you are done. For 60: 60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5, 5 is prime. So 60 = 2² × 3 × 5.
What is the fastest way to find prime factors by hand?
Use the divisibility rules: check 2 (even), 3 (sum of digits divisible by 3), and 5 (ends in 0 or 5) first. For larger numbers, use a factor tree or trial division up to the square root of the number. The calculator above uses trial division and is much faster for any number over 100.
How do I find the GCF using prime factorization?
Find the prime factorization of each number. Identify the common prime factors and multiply them together using the smallest exponent that appears in any of the factorizations. For example, 48 = 2&sup4; × 3 and 60 = 2² × 3 × 5, so the GCF is 2² × 3 = 12.
Can every number above 1 be factorised into primes?
Yes. The fundamental theorem of arithmetic states that every integer greater than 1 has a unique prime factorisation (ignoring the order of factors). This is why prime factorisation is a reliable method for understanding the building blocks of any number.
What is a factor tree?
A factor tree is a visual method for prime factorisation. Write the number at the top, draw two branches down to a pair of factors, and continue branching each composite factor until every branch ends in a prime number. The primes at the bottom are the prime factors of the original number.
What is the difference between factors and prime factors?
Factors are all the whole numbers that divide evenly into a number. Prime factors are a subset that are prime numbers (only divisible by 1 and themselves). For 60, the factors are 1,2,3,4,5,6,10,12,15,20,30,60, but the prime factors are only 2, 2, 3, and 5.