Question

Which of the following has the most number of divisors?

• A. 99
• B. 101
• C. 176
• D. 182
• E. 87

Answer 1

The correct option is C

176

99 = 1 $\times$ 3 $\times$ 3 $\times$ 11
101 = 1 $\times$ 101
176 =1 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 11
182 = 1 $\times$ 2 $\times$ 7 $\times$ 13
87 = 1 $\times$ 3 $\times$ 29

So, divisors of 99 are 1, 3, 9, 11, 33 and 99; divisors of 101 are 1 and 101; divisors of 176 are 1, 2, 4, 8, 16, 22, 44, 88 and 176; divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182; divisors of 87 are 1,3,29 and 87. Hence, 176 has the most number of divisors.