Question

The sum of the exponent of the prime factors in the prime factorization of $3240$ is,

Answer 1

Sum of the exponent of the prime factors in the prime factorization of the given number.

The prime factorization of $3240$ is written as,

$$\begin{gathered} 3240=2\times 2\times 2\times 3\times 3\times 3\times 3\times 5 \\ \Rightarrow =2^3\times 3^4+5^1 \end{gathered}$$

The exponent of prime factors are $3,4,1$.

The sum of the exponent$=3+4+1=8$

Hence, the sum of the exponents is $8$.