In mathematics, GCF is used for making fractions simpler. GCF is used to find the greatest divisor of the given numbers. It is very essential for different purposes in the field of mathematics. It can make the calculations simpler. By using GCF we can solve any problem easily.

In this post, we will learn how to find the GCF of four or more terms with a lot of examples.

What is GCF?

GCF is the greatest common factor or divisor that two or more numbers have. The mathematical problems are simplified by using GCF. Like fractions can be simplified easily by using GCF. For example, if a fraction is given like 42/49.

Then we have to take the GCF of the numerator and the denominator and then divide the numerator and the denominator with the calculated GCF to simplify the fraction. In the given example, the GCF of 42 and 49 is 7. Now use it in the above fraction, (42/7) / (49/7) = 6/7.

By taking the GCF of fractions, the calculation of the fractions becomes easier. As fractions are used widely in problems, we must have to know how to simplify the fractions.

Methods to find GCF

There are various methods used to determine the greatest common factors of two or more numbers. Such as,

(i) List of factors
(ii) Prime factorization
(iii) Division method

These methods are used to find the greatest common factors. We can easily find the GCF of two or more numbers by using these methods.

Calculating GCF of more than four numbers?

We can find the GCF of four or more numbers by using the list of factors and prime factorization methods. Let’s take examples of four or more numbers to calculate the GCF.

Example 1: By list of factors.

Find the GCF of 63, 39, 33, and 48 by using the list of factors method?

Solution
Step 1: First of all, take the numbers given in the problem.
63, 39, 33, and 48
Step 2: Determine the factors of 63, 39, 33, and 48.
Divisors of 63 = 1, 3, 7, 9, 21, 63
Divisors of 39 = 1, 3, 13, 39
Divisors of 33 = 1, 3, 11, 33
Divisors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 4
Step 3: Take the similar factors of 63, 39, 33, and 48.
Similar factors of 63, 39, 33, and 48 = 1, 3

Step 4: Now choose the greatest number from the common factor.
Greatest common factors of 63, 39, 33, and 48 = 3

Example 2
Find the GCF of 15, 30, 45, 70, and 85 by using the list of factors method?
Solution

Step 1: First of all, take the numbers given in the problem.
15, 30, 45, 70 and 85

Step 2: Determine the factors of 15, 30, 45, 70 and 85.
Divisors of 15 = 1, 3, 5, 15
Divisors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Divisors of 45 = 1, 3, 5, 9, 15, 45
Divisors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
Divisors of 85 = 1, 5, 17, 85

Step 3: Take the similar factors of 15, 30, 45, 70 and 85.
Similar factors of 15, 30, 45, 70 and 85 = 1, 5

Step 4: Now choose the greatest number from the common factor.
Greatest common factors of 15, 30, 45, 70 and 85 = 5

Example 3
Find the GCF of 21, 27, 36, 45, 54, and 63 by using the list of factors method?

Solution
Step 1: First of all, take the numbers given in the problem. 21, 27, 36, 45, 54, and 63

Step 2: Determine the factors of 21, 27, 36, 45, 54, and 63.

Divisors of 21 = 1, 3, 7, 21
Divisors of 27 = 1, 3, 9, 27
Divisors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Divisors of 45 = 1, 3, 5, 9, 15, 45
Divisors of 54 = 1, 2, 3, 6, 9, 18, 27, 54
Divisors of 63 = 1, 3, 7, 9, 21, 63
Step 3: Take the similar factors of 21, 27, 36, 45, 54, and 63.
Similar factors of 21, 27, 36, 45, 54, and 63 = 1, 3

Step 4: Now choose the greatest number from common factor.
Greatest common factors of 21, 27, 36, 45, 54, and 63 = 3

By increasing the numbers, it becomes rather tough to solve such a large calculation. In this
case a GCF calculator is very helpful in finding the greatest common factor of more than four numbers.

Example 4: By prime factorization.
Find the GCF of 22, 66, 55, and 110 by using prime factorization?

Solution

Step 1: First of all, take the numbers given in the problem.
22, 66, 55, and 110

Step 2: Now determine the prime factors of 22, 66, 55, and 110.

Factors of 22 by prime factorization = 2 x 11
Factors of 66 by prime factorization = 2 x 3 x 11
Factors of 55 by prime factorization = 2 x 2 x 2 x 11
Factors of 110 by prime factorization = 2 x 5 x 11

Step 3: Take the similar factor from the prime factor.
Similar factor of 22, 66, 55, and 110 = 2 x 11

Step 4: Now multiply the similar factors.
GCF of 22, 66, 55, and 110 = 22

Example 5
Find the GCF of 84, 136, 152, 160, and 180 by using prime factorization?

Solution
Step 1: First of all, take the numbers given in the problem.
84, 136, 152, 160, and 180

Step 2: Now determine the prime factors of 84, 136, 152, 160, and 180.
Factors of 84 by prime factorization = 2 x 2 x 3 x 7
Factors of 136 by prime factorization = 2 x 2 x 2 x 17
Factors of 152 by prime factorization = 2 x 2 x 2 x 19

Factors of 160 by prime factorization = 2 x 2 x 2 x 2 x 2 x 5
Factors of 180 by prime factorization = 2 x 2 x 3 x 3 x 5

Step 3: Take the similar factor from the prime factor.
Similar factor of 84, 136, 152, 160, and 180= 2 x 2
Step 4: Now multiply the similar factors.

GCF of 84, 136, 152, 160, and 180 = 4

Summary

The GCF is used to find the exact divisors of numbers. The GCF of four or more numbers is easily calculated by the list of factors or the prime factorization method. But we are unable to solve the GCF by using the division method. Because GCF can be calculated by the division method just for 2 or 3 numbers.