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.

**Mahesh**

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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?

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