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Chapter 4: Q9. (page 177)

Find the relationship between the resulting quotients when you divide two numbers by their greatest common factor.

Short Answer

Expert verified

The resulting quotient should be a relatively prime.

Step by step solution

01

Step -1 - Apply the concept of   GCF.

In this, simply use the concept of finding the GCF by doing the factors of the number and find the factor which is common and greatest from them.

02

Step -2 – Explanation of the statement

Since, when the two number is divided by its greatest common factor then the quotient that comes after dividing should be relatively prime to each other.

03

Step -3 – Explanation by taking example

Now, taking two numbers such as 4,8.

Factors of4 is4=1脳4

Factors of 8 is8=2脳4

Greatest common factor of 4 and 8is 4

Now, divide both the numbers by their greatest common factor.

44=1and84=2

Here, resulting quotients are1and2 , which are relatively prime.

Hence, it can be concluded that when two numbers are divided by their greatest common factor, then the resulting quotients are relatively prime to each other.

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