Question

Which of the following has the most number of divisors?

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

Answer 1

Answer: (C)

$176$

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