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(#M40008436) SELF question self Keep an EYE

Which of the following has the most number of divisors?

A. 99 B. 101
C. 176 D. 182

niru (13 years ago)

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Sanjana Patnaik  (13 years ago)

No. of divisors can be found out
from the index of prime factors of that number
99=3^2*11^1( No. of divisors=3*2=6)( simply increase 1 of the index of prime factor and multiply)
101=No. of divisors=2 as the same is the prime No.
176=2^4+11^1( No. of divisors=5*2=10
182=2^1*7^1*13^1(No. of divisors=2*2*2=8
Hence, 176 has 10 divisors

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Vignesh  (13 years ago)

C. 176 number have more number of divisors.

Divisiors 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.

So, C.176 is the answer

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