How to find the GCF
Prime factorization: multiply the primes the numbers share, using the lowest power of each. 48 = 2⁴·3 and 180 = 2²·3²·5, so GCF = 2²·3 = 12.
Euclid’s algorithm: replace the larger number with the remainder of dividing it by the smaller, until the remainder is 0. 180 mod 48 = 36, 48 mod 36 = 12, 36 mod 12 = 0 → GCF = 12. This is fast even for very large numbers.
Using the GCF to simplify fractions
Divide the numerator and denominator by their GCF: 48/180 ÷ 12 = 4/15.
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Frequently asked questions
Is GCF the same as GCD and HCF?
Yes — greatest common factor, greatest common divisor and highest common factor are three names for the same thing.
What is the GCF of two numbers with no common factors?
1. Such numbers are called coprime.