Number System
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Q.

Which of the following has most number of divisors?

 A.

99

 B.

101

 C.

176

 D.

182

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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.


(9) Comment(s)


Mahesh
 ()

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


Avinash Jampala
 ()

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

Avinash Jampala
 ()

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

Kaushik
 ()

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


Gopal
 ()

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


Lohit
 ()

Could you please elaborate more.
That would be great.

Ekta Mishra
 ()

I think lcm method is good


Vinay
 ()

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.


Shresth
 ()

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 Sad

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