**Answer:** 48.

Which has 10 divisors (1, 2, 3, 4, 6, 8, 12, 16, 24, 48).

You can use the prime factors of any number to find how many divisors it has. For example:

21 = 3 x 7. In any divisor, each factor might appear zero or once. We could therefore choose 3 in two ways, and choose 7 in two ways. This gives us 2 x 2 ways to choose the prime factors, which means there are 4 divisors (1, 3, 7, 21).

Another example, 60 = 2 x 2 x 3 x 5. In any divisor we can choose 2 in three ways (zero, once or twice), choose 3 in two ways (zero or once), and choose 5 in two ways (zero or once). This gives us 3 x 2 x 2 possible combinations = 12 divisors.

We can apply this method to any number and could try all numbers below 50. However, with a little educated guesswork the required number will have 2 and 3 as part of its prime factors if it has lots of divisors.

48's prime factors are 2 x 2 x 2 x 2 x 3. So we can choose 2 in five ways (zero, once, ... , or four times), and choose 3 in two ways (zero or once). This gives us 5 x 2 possible combinations, and therefore 10 divisors. The most of any number below 50. QED.