Introduction to greatest common factor of two number

Introduction to greatest common factor of two number:

In mathematics, the greatest common divisor (gcd), also known as the greatest common denominator, greatest common factor (gcf), or highest common factor (hcf), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.

Through this article we are going to learn about how to find the greatest common factor of two numbers and some solved problems on greatest common factors of two numbers.

Greatest Common Factors of Two Numbers:

Steps to find greatest common factor:

Step 1: Write down the two numbers that we want to find greatest common factor.

Step 2: Find the factors of  given two numbers.

Step 3: Write down the common factor of both numbers.

Step 4: Choose the largest number from the common factor. That number is known as greatest common factor of  the two numbers.

Step 5: If there is no common factor , 1 is the GCF of the given two numbers.

Solved Problems on Greatest Common Factors of Two Numbers:

Problem 1:

Find the greatest common factor of the following two numbers 30, 60.

Solution:

Given, Numbers 30 , 60

We need to find the greatest common factor of 30, 60.

Step 1: Write down the two numbers that we want to find greatest common factor.

30 , 60

Step 2: Find the factors of  given two numbers.

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

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30,60

Step 3: Write down the common factor of both numbers.

Common factors of 30 and 60 is 1, 2, 3, 5, 6, 10, 15, 30

Step 4: Choose the largest number from the common factor. That number is known as greatest common factor of  the two numbers.

Greatest common factor of 30 and 60 is 30.

Problem 2:

Find the greatest common factor of the following two numbers 180 , 256

Solution:

Given, Numbers 180, 256

We need to find the greatest common factor of 180, 256

Step 1: Write down the two numbers that we want to find greatest common factor.

180, 256

Step 2: Find the factors of  given two numbers.

Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

Factors of 256 = 1, 2, 4, 8, 16, 32, 64, 128, 256

Step 3: Write down the common factor of both numbers.

Common factors of 180 and 256 is 1, 2, 4

Step 4: Choose the largest number from the common factor. That number is known as greatest common factor of  the two numbers.

Greatest Common factors of 180 and 256 is 4.

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Practice Problems on Greatest Common Factors of Two Numbers:

Problems:

1.Find the greatest common factor of the following two numbers 18 , 26

2.Find the greatest common factor of the following two numbers 56,90

Solution:

1. 2

2. 2