Aptitude Discussion

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 |

**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**.

**Nitin**

*()
*

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.

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

So $N = 12$

$N-1 = 11$

11 has only 2 factors. 1 and 11.