Aptitude Discussion

Q. |
Which of the following has most number of divisors? |

✖ A. |
99 |

✖ B. |
101 |

✔ C. |
176 |

✖ D. |
182 |

**Solution:**

Option(**C**) is correct

Divisors of $99 = 1, 3, 9, 11, 33, 99$

Divisors of $101 = 1,101$

Divisors of $176 = 1, 2, 4, 8, 11, 22, 44, 88, 176$

Divisors of $182 = 1, 2, 7, 13, 14, 26, 91, 182$

Therefore **176** has most number of divisors.

**Aditya**

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**Mahesh**

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find the no of divisors using as below.

1. Prime factorize the no $182=2^1*7^1*13^1$

2. Increase the power of each prime factor by 1 and multiply

i.e power of $2*2*2=6$ divisors

$176=2^4*11^1$

therefore $5*2= 10$ divisors

correction: $2*2*2= 8$ divisors

Also, 176 as only 9 divisors according to the given solution so how come its 10 divisors $(5 * 2)$

this method is correct 10 divisors. with 16 is also a divisor

**Gopal**

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take l.c.m. of no

99-3*3*11

101-1

__176-2*2*2*2*11__

182-2*7*13

so the answer is 176

Could you please elaborate more.

That would be great.

I think lcm method is good

**Vinay**

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can you tell me a simpler way to solve the same question.Is there an alternate method where we don't have to write all the divisors.

Well I tried searching a lot about the same thing i.e. way to solve ths in a simpler way. I guess there is n way out but to solve the questions by finding all the divisors individually

Good thing is it's not that demanding is it?

well...

99=3^2*11,by(p+1)(q+1).. total divisors=(2+1)(1+1)=6

similarly ,101 has 1

,176 has 10

and 182 has 4 divisors

hence,176 is the answer