Number System
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Q.

$N$ is the smallest number that has 5 factors. How many factors does $(N - 1)$ have?

 A.

2

 B.

3

 C.

4

 D.

5

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Solution:
Option(C) is correct

A number that has 5 factors has to be of the form $p^4$ where '$p$' is a prime number.

The smallest such number is $2^4 = 16$

Therefore, $N - 1 = 15.$ 

The factors of 15 are $1, 3, 5, 15.$

So, $N - 1$ has 4 factors.


(2) Comment(s)


Nitin
 ()

12 has five factors. 1,2,3,4,12.

So $N = 12$

$N-1 = 11$

11 has only 2 factors. 1 and 11.


Rupesh
 ()

Nitin, 12 has six factors: 1, 2, 3, 4, 6, 12

So value of N can not be 12 as number of factors has to be 5 only.

Value of N has to be 15 only. Cool