Find the number of divisors of the number.
-$2 ^ { 5 } \cdot 3 ^ { 6 } \cdot 5 ^ { 2 }$
A) 120
B) 126
C) 60
D) 90

Question

Quizplus · Accepted Answer

The number of divisors of a number $n = p_1^{a_1} \cdot p_2^{a_2} \cdot \ldots \cdot p_k^{a_k}$, where $p_1, p_2, \ldots, p_k$ are prime factors and $a_1, a_2, \ldots, a_k$ are their respective powers, is given by $(a_1 + 1)(a_2 + 1) \ldots (a_k + 1)$. For $2^5 \cdot 3^6 \cdot 5^2$, this gives $(5+1)(6+1)(2+1) = 6 \cdot 7 \cdot 3 = 126$.

Find the Number of Divisors of the Number 25⋅36⋅522 ^ { 5 } \cdot 3 ^ { 6 } \cdot 5 ^ { 2 }25⋅36⋅52

Find the Number of Divisors of the Number $2 ^ { 5 } \cdot 3 ^ { 6 } \cdot 5 ^ { 2 }$