Definition: The greatest common factor of two or more whole numbers is the largest whole number that divides every one of them with no remainder.
What is the GCF?
A factor divides a number evenly. The GCF of a set of numbers is the biggest factor they all share.
How do you find it?
List factors. For 36 and 60:
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The common ones are 1, 2, 3, 4, 6, and 12. The greatest is 12.
You can also use prime factorization. Since 36 = 22 x 32 and 60 = 22 x 3 x 5, take the lowest power of each shared prime: 22 x 3 = 12.
Where is it used?
Mathbot packs 36 bolts and 60 nuts into identical kits with nothing left over. The most kits he can make is 12, each holding 3 bolts and 5 nuts.
What is a common mix-up?
Confusing GCF with LCM. The GCF is never larger than the smallest number in the set, while the LCM is never smaller than the largest.
Example: The GCF of 28 and 42 is 14.