GCF Calculator
Choose a fast answer or optional teaching.
Step-by-step
Practice Mode
Find the greatest shared factor.
What to understand
The GCF is the largest whole number that divides both inputs with no remainder.
⚡ Smart GCF Shortcuts
Factor-pair shortcut: Test factor pairs from the outside toward the middle. Once the pair numbers meet or cross, stop.
Divisibility shortcut: Check easy shared factors first: 2 for even numbers, 5 for numbers ending in 0 or 5, 10 for numbers ending in 0, and 3 when the digit sum is divisible by 3.
Large-number shortcut: For larger numbers, repeated remainders can find the GCF efficiently: replace the larger number with the remainder after division until the remainder is 0.
When not to use: For young learners or small numbers, factor lists may be clearer than a faster algorithm.
Check: The GCF must divide both original numbers evenly.