Prime factorization of $600 = 2^3 \times 3 \times 5^2.$
Total no of divisors $= (3+1) (1+1) (2+1) = 4 \times 2 \times 3 = 24$ divisors
Here, we are choosing either $0, 1 , 2$ or $3, 2's$ so $3 + 1 = 4$ choices for $2$ and so on for all.
In case we do not choose any of the above factors, we get $1$ as divisor!