Greatest Common Factor Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy

Find the GCF of

48

and

36

Solution

1
Prime-factor each number: $48 = 2^4 \times 3$ and $36 = 2^2 \times 3^2$ .
2
Identify the common prime factors and keep the smaller exponent for each: $2^2$ and $3^1$ .
3
Multiply those shared factors: $2^2 \times 3 = 4 \times 3 = 12$ , so the GCF is $12$ .

Answer

12

The GCF is the product of shared prime factors, each raised to the lowest power appearing in either factorization. The GCF is useful for simplifying fractions.

About Greatest Common Factor

The greatest common factor (GCF) of two or more numbers is the largest positive integer that divides each of them evenly, with no remainder. It is also called the greatest common divisor (GCD).

Learn more about Greatest Common Factor →

More Greatest Common Factor Examples

Example 2 medium

Find the GCF of [formula], [formula], and [formula].

Example 3 easy

Find the GCF of [formula] and [formula].

Example 4 easy

A teacher has ribbons of lengths [formula] cm and [formula] cm. She wants to cut them into the longe

← All Greatest Common Factor Examples Greatest Common Factor Concept

Related Concepts

Factors Divisibility Intuition Simplification Least Common Multiple