# The smallest value of x for which $\dfrac{7}{{\text{x}}}$ is an integer is

$

{\text{A}}{\text{. 1}} \\

{\text{B}}{\text{. - 1}} \\

{\text{C}}{\text{. 7}} \\

{\text{D}}{\text{. - 7}} \\

$

Last updated date: 21st Mar 2023

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Answer

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Hint: All values of x will give an integer value for the fraction. By number system -7 is the smallest value in all of them.

Complete step-by-step answer:

We have a fraction, $\dfrac{7}{{\text{x}}}$. We need to find x such that the fraction becomes integer.

As we are dividing 7 by another number, it needs to be either multiple of 7 or 1 or -1. Since, 7 is a prime number.

We have four options 1, -1, 7 and -7. All the options are either the multiple of 7 or -1 or 1.

So, all options will give an integer after dividing 7 by each of them.

We need to find the smallest value of x. So, we know that by number system.

-7<-6<-5<-4<-3<-2<-1<0<1<2<3<4<5<6<7

So, -7 is the smallest value of x.

Note: Always pay attention to each word of the question. A prime number is only divisible by itself or 1.

e.g. 2,3,7,etc.

Complete step-by-step answer:

We have a fraction, $\dfrac{7}{{\text{x}}}$. We need to find x such that the fraction becomes integer.

As we are dividing 7 by another number, it needs to be either multiple of 7 or 1 or -1. Since, 7 is a prime number.

We have four options 1, -1, 7 and -7. All the options are either the multiple of 7 or -1 or 1.

So, all options will give an integer after dividing 7 by each of them.

We need to find the smallest value of x. So, we know that by number system.

-7<-6<-5<-4<-3<-2<-1<0<1<2<3<4<5<6<7

So, -7 is the smallest value of x.

Note: Always pay attention to each word of the question. A prime number is only divisible by itself or 1.

e.g. 2,3,7,etc.

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