Chapter 4.2, Problem 50E

To determine

To find the GCF of a and b and explain it.

Answer to Problem 50E

‘a’ is the GCF of ‘a’ and ‘b’.

Explanation of Solution

Given Information:a and b are non zero whole numbers and a is a factor of b .

Formula Used:if a is a factor of b, then the GCF between the two numbers will be a. This is because, as ‘a’ is a factor of ‘b’, then ‘a’ cannot have a factor which is greater than itself.

Calculation:

To prove this, lets take 3 examples.

ExampleI Lets assume a=6 & b=42. Now

The factors of 6 are: 1, 2, 3, 6

The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42

Then the greatest common factor is 6, i.e. ‘a’.

ExampleII Lets assume a=7 & b=42 Now

The factors of 7 are: 1, 7

The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42

Then the greatest common factor is 7, i.e. ‘a’.

ExampleIII Lets assume a=8 & b=48 . Now

The factors of 8 are: 1, 2, 4, 8

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Then the greatest common factor is 8, i.e. ‘a’.

Therefore, for all 3 values of ‘a’ i.e. 6, 7, and 8, the GCF for all three numbers were 6, 7 and 8 respectively. By this can conclude that a number which is a factor of another number, is the GCF between the two of them.

Hence proved.