FractionReference

Greatest common factor

The largest number that divides all of them evenly. Type two or more whole numbers, separated by commas or spaces — the answer comes with the factor tables it was built from, because the method is the useful part.

Try:

Common questions

What is the greatest common factor?
The largest whole number that divides every one of your numbers with nothing left over. For 24 and 64 it is 8, because 8 divides both and nothing larger does.
How do I find the GCF by hand?
Factor each number into primes, then take the lowest power of each prime that appears in all of them and multiply. 24 is 2³ × 3 and 64 is 2⁶, so the shared part is 2³ = 8. The table on this page shows exactly that.
What is the GCF used for?
Simplifying fractions. Dividing the top and bottom of 24/64 by their GCF of 8 gives 3/8 in one step — which is the whole of what "reduce to lowest terms" means.
What if the numbers share no factors?
Then the GCF is 1 and the numbers are called coprime. A fraction built from two coprime numbers is already in lowest terms — there is nothing to divide out.

Related

Least common multipleThe other half: the smallest number they all divide into. Simplify a fractionThe GCF, applied — 24/64 → 3/8. Equivalent fractionsThe same move in reverse.
Where this comes from. Exact rational arithmetic on the values shown — fractions are pairs of integers until display, and inch–metric conversion uses 25.4 mm to the inch, exact by definition since 1959. Factorisation is by trial division, exact for every number this tool accepts. See the full methodology.