Question

How many non-prime factors are in the number $N=2^5\times 3^7\times 9^2\times {11}^4\times {13}^3$.

Answer 1

Given

$N=2^5\times 3^7\times 9^2\times {11}^4\times {13}^3$

It can also be written as

$N=2^5\times 3^{11}\times \times {11}^4\times {13}^3$

To calculate total number of factors adding 1 to each exponent and multiplying, we get

Total number of factors$=6\times 12\times 5\times 4=1440$

Number of prime factors$=4$

So,

Number of non-prime factors$=1440-4=1436$

Therefore total number of non prime factors are $1436$.