Chapter 4.2, Problem 48E

To determine

  $$To identify: The possible value of n .

Answer to Problem 48E

The value of n is 6.

And other possible value of n is $12,18,24,36,\mathrm{...}$

Explanation of Solution

Given information: The greatest common factor of 30 and a number is n is 6.

Since,

  $\gcd \left(30,n\right)=6$

So,

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

Factor of 6 = 1, 2, 3

There is possible common factor of 30 and 6 is $2\times 3$ that is 6.

  $\Rightarrow n=6$

And other possible values of n are the multiple of 6.

Then,

  $12,18,24,36,\mathrm{...}$

The number 30 can not be included in this since 30 is a factor of 5 also.

Conclusion:

The value of n is 6.

And other possible value of n is $12,18,24,36,\mathrm{...}$