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GCF Formula

The greatest common factor (GCF) of two numbers is the largest possible number that divides both the numbers exactly. The properties of GCF are GCF of two or more numbers divides each of the numbers without a remainder, GCF of two or more numbers is a factor of each of the numbers, GCF of two or more numbers is always less than or equal to each of the numbers, and GCF of two or more prime numbers is 1 always. Let us learn more about the GCF formula along with the solved examples.

What Is the GCF Formula?

There are 3 methods to calculate the GCF of two numbers first is GCF by listing out the common factors, the second method is GCF by prime factorization, and the third method is GCF by division method. Let us understand these methods better using solved examples.

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Examples Using GCF Formula

Example 1: What is the GCF of 30 and 42? Solve by using the GCF formula.

Solution:

List the factors of each number.

Factors of 30 - 1, 2, 3, 5, 6, 10, 15, 30

Factors of 42 - 1, 2, 3, 6, 7, 14, 21, 42

GCF using common factors

6 is a common factor and the greatest one.

Hence, the GCF of 30 and 42 is 6.

Answer: GCF of 30 and 42 is 6.

Example 2: What is the GCF of 60 and 90? Solve by using the GCF formula.

Solution:

Represent the numbers in the prime factored form.

60 = 2 × 2 × 3 × 5

90 = 2 × 3 × 3 × 5

GCF is the product of the factors that are common to each of the given numbers.

Thus, GCF of 60 and 90 = 2 × 3 × 5 = 30.

Answer: GCF of 60 and 90 is 30.