What is GCF in Math

Introduction to gcf in math:

In mathematics, Gcf is used to simplify the common fractions and carrying out basic operations. The greatest common divisor (gcd), as well-known as the greatest common factor (gcf), greatest common denominator, or highest common factor (hcf), of two or more non-zero integers, is the largest positive integer that divide the numbers without a remainder. In mathematics “Greatest Common Factor” short form gcf. GCF of those numbers is largest factor which commonly divides the specified set of numbers (two or more).


Examples problem for gcf in math:


1. Find the gcf of 8, 10, 6, 14 and 16.

Solution:

Given numbers are 8, 10, 6, 14 and 16.

The Greatest Common Factor (GCF) of the numbers 8, 10, 6, 14 and 16 is 2.

2 is the greatest number that divides common into all of them.

Gcf of this problem is 2.

2. Find the gcf of 150, 250,300 and 350.

Solution:

Given numbers are 150, 250, 300 and 350.

The Greatest Common Factor (GCF) of the numbers 150, 250, 300 and 350 is 50.

50 is the greatest number that divides common into all of them.

Gcf of this problem is 50.

3. Find the gcf of 25, 55, 17, 16 and 50.

Solution:

Given numbers are 25, 55, 17, 16 and 50.

The Greatest Common Factor (GCF) of the numbers 25, 55, 17, 16 and 50 is 1.

1 is the greatest number that divides common into all of them.

Gcf of this problem is 1.

4. Find the gcf of 15, 45, 18, 27 and 60.

Solution:

Given numbers are 15, 45, 18, 27 and 60.

The Greatest Common Factor (GCF) of the numbers 15, 45, 18, 27 and 60 is 3.

3 is the greatest number that divides common into all of them.

Gcf of this problem is 3.

5. Find the gcf of 10, 30, 50, 70 and 80.

Solution:

Given numbers are 10, 30, 50, 70 and 80.

The Greatest Common Factor (GCF) of the numbers 10, 30, 50, 70 and 80 is 10.

10 is the greatest number that divides common into all of them.

Gcf of this problem is 10.

6. Find the Greatest Common Factor (gcf) of 14, 24 and 42.

lowest Factors of 14: 1,2,7,14
lowest Factors of  24 : 1, 2,4, 6,8,12,24
lowest Factors of  42  : 1, 2, 3, 6, 7, 14, 21, 42

Common Factors: 1, 2.
1, 2 divides 14, 24, 42 therefore they are common factors.

Answers for gcf = 2

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Practice problems for gcf in math:


1. Find the gcf of 20, 52, 10, 16 and 50.

Answers for gcf = 2

2. Find the gcf of 25, 55, 15, 35 and 50.

Answers for gcf = 5

3. Find the gcf of 6, 12, 15, 21 and 30.

Answers for gcf = 3