Prime Factorization Calculator
Find the prime factorization of any number with steps, check if a number is prime, list all divisors and prime numbers. Free online prime factor calculator.
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Part of the toolkit
How to use Prime Factorization Calculator
- 1Type any whole number up to 9 quadrillion (16 digits)
- 2Read its prime factorization in exponent form, whether it's prime, and the step-by-step division ladder
- 3See all divisors, their count and sum, the nearest primes, or switch to List prime numbers to get every prime in a range
Frequently asked questions
How do you find the prime factorization of a number?▾
Divide by the smallest prime that goes in evenly, then repeat with the result until you reach 1. For 360: 360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, ÷ 3 = 15, ÷ 3 = 5, ÷ 5 = 1. So 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5.
How do I know if a number is prime?▾
A prime has exactly two divisors, 1 and itself. Check whether any prime up to its square root divides it evenly; if none does, it's prime. For 97, √97 ≈ 9.8 and none of 2, 3, 5 or 7 divides it, so 97 is prime.
Is 1 a prime number?▾
No. 1 is neither prime nor composite because it has only one divisor. Mathematicians exclude it so that every whole number greater than 1 has exactly one prime factorization. The smallest prime is 2, the only even prime.
How many divisors does a number have?▾
Add 1 to each exponent in the prime factorization and multiply. 360 = 2³ × 3² × 5¹ has (3+1)(2+1)(1+1) = 24 divisors.
How many prime numbers are there up to 100?▾
There are 25 primes below 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. Up to 1,000 there are 168, and up to 1,000,000 there are 78,498.
What is a perfect number?▾
A number equal to the sum of its divisors other than itself, like 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14. If that sum is larger the number is abundant (12), and if smaller it is deficient (8). The calculator tells you which one your number is.
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