Find the GCF Using Prime Factorization (GCF & LCM, 2026)

To find the GCF using prime factorization, break each number into primes and multiply the lowest power of every prime they share. It is the most reliable way to find the greatest common factor — and the same factorizations also hand you the LCM for free.

Below you will see the method step by step, how it connects GCF and LCM, and worked examples you can check in the GCD / GCF Calculator.

GCF, GCD and HCF — same thing

The greatest common factor (GCF) is the largest whole number that divides every input with no remainder. It is identical to the GCD (greatest common divisor) and the HCF (highest common factor) — three names for one idea.

The prime-factorization method

Three steps: (1) write each number as a product of primes; (2) find the primes that appear in all of them; (3) for each shared prime, take the lowest power and multiply. That product is the GCF.

Worked example: GCF of 48 and 60

48 = 2⁴ × 3 and 60 = 2² × 3 × 5. The shared primes are 2 and 3. Take the lowest powers: 2² (from 60) and 3¹. So GCF = 2² × 3 = 12. Check: 48 ÷ 12 = 4 and 60 ÷ 12 = 5 — both whole numbers. ✓

Get the LCM at the same time

Using the same factorizations, the LCM takes the highest power of every prime that appears: 2⁴ × 3 × 5 = 240. Notice that GCF × LCM = 12 × 240 = 2,880 = 48 × 60. This identity, GCF × LCM = a × b, is why a single calculation gives you both — try it in the LCM Calculator.

When to use Euclid instead

For very large numbers, factoring is slow. The Euclidean algorithm finds the GCF in a handful of divisions without any factorization — it is the method computers use.