Glossary
greatest common factor
The greatest common factor of two numbers is the largest number that divides both evenly. It is used to simplify a fraction to lowest terms.
The greatest common factor of two numbers is the largest whole number that divides both of them with nothing left over. For 18 and 24 the common factors are 1, 2, 3 and 6, so the greatest common factor is 6.
There are two reliable ways to find it. List the factors of each number and take the largest they share, which is fine for small numbers. Or factor both into primes and multiply the primes the two lists have in common: 18 is 2 × 3 × 3 and 24 is 2 × 2 × 2 × 3, so the shared primes are one 2 and one 3 and the greatest common factor is 6.
Its job in arithmetic is simplifying fractions: divide the top and the bottom by their greatest common factor and the fraction is in lowest terms (18/24 becomes 3/4). Its companion is the least common multiple, and the two are easy to confuse — one divides, the other is divided into. Both come up whenever a question involves equal groups, shared factors or adding fractions with unlike denominators.
Taught in
Related terms
- least common multiple — The least common multiple of two numbers is the smallest number both divide into evenly. It is the common denominator when you add fractions.
- prime number — A prime number has exactly two factors: 1 and itself. 2, 3, 5, 7 and 11 are prime; 1 is not, and 9 is not because 3 divides it.
Source: Official ASVAB — subtest descriptions (what each subtest asks) and the CAT-ASVAB scored-question counts (accessed 2026-09)