87. How many different divisors does the number have a) 800; b) 126000?
87. a) Since $800=2^{5} \cdot 5^{2}$, the power of two can be part of the divisor of this number in six ways $\left(2^{0}, 2^{1}, 2^{2}, 2^{3}, 2^{4}, 2^{5}\right)$, and the power of five in three ways ( $5^{0}, 5^{1}, 5^{2}$ ). Therefore, by the rule of multiplication, we get that the number 800 has $6 \cdot 3=18$ different divisors.

b) Since $126000=2^{4} \cdot 3^{2} \cdot 5^{3} \cdot 7$, the number of divisors of this number is $(4+1)(2+1)(3+1)(1+1)=120$.