Math

Prime Factors Calculator

Find the Prime Factors of Any Number

Prime factors are the prime numbers that multiply together to give the original number. This calculator uses trial division to find all prime factors instantly, displaying them in exponential notation with a visual factor tree.

Prime Factorization Tips

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Try an Example

Pick a scenario to see how the calculator works, then adjust the values

Highly Composite Number

Factor 360, a highly composite number with many divisors.

Key values: 360 = 2^3 x 3^2 x 5 · 24 divisors · phi(360) = 96

Large Prime

Check if 7919 is prime (it is -- the 1000th prime number).

Key values: 7919 is prime · 2 divisors · phi(7919) = 7918

GCD and LCM

Compute the GCD and LCM of 84 and 120.

Key values: 84 = 2^2 x 3 x 7 · 120 = 2^3 x 3 x 5 · GCD = 12, LCM = 840

Find the Prime Factorization

Enter an integer greater than 1 to see its prime factorization, factor tree, and divisors.

Documentation

This calculator is also known as Prime Factors Calculator.

Read the complete guide

Prime Factors vs Factor Pairs

Prime factors are the building blocks: 12 = 2² × 3. Factor pairs are any two numbers that multiply to give 12: (1,12), (2,6), (3,4). Prime factorization is unique; factor pairs are not.

Examples

Prime Factors of 360

Find the prime decomposition of 360

360 = 2³ × 3² × 5. The prime factors are 2, 3, and 5.

Key takeaway: The exponential form shows both which primes appear and how many times each divides the number.

Working with Prime Factors

Prime factors unlock many arithmetic shortcuts.

To simplify a fraction, find the prime factors of both numerator and denominator, then cancel shared factors
To find the LCM of two numbers, take each prime factor at its highest exponent
To count all divisors, add 1 to each exponent and multiply the results

Frequently Asked Questions about Prime Factors Calculator

What are prime factors?

Prime factors are the prime numbers that divide a given number exactly. Every integer > 1 can be expressed as a unique product of prime factors.

How do I find prime factors by hand?

Divide the number by 2 repeatedly until it’s odd, then by 3, then by 5, and so on. Each time a prime divides evenly, it is a prime factor. Stop when the quotient is 1.