Which number among the following has the greatest quantity of divisors?

Explanation

Let's analyze the divisors for each number: 99 factors into 3² × 11, giving divisors 1, 3, 9, 11, 33, and 99 (6 divisors). 101 is a prime number, so its divisors are only 1 and 101 (2 divisors). 176 breaks down to 2⁴ × 11, resulting in divisors 1, 2, 4, 8, 16, 11, 22, 44, 88, and 176 (10 divisors). 182 factors into 2 × 7 × 13, yielding divisors 1, 2, 7, 13, 14, 26, 91, and 182 (8 divisors). Therefore, 176 has the highest number of divisors among the options.