jmc

The prime factorization of 48 is $2^4\cdot 3$. Since the greatest common factor is 24, that means the other number also has the factors $2^3$ and 3 but not a fourth 2. When we divide 240 by 48, we get 5. The factors $2^3$ and 3 of the other number are covered by the factors of 48, but the factor 5 must come from the other number. So, the other number is $2^3\cdot 3\cdot 5=\boxed{120}$.