Question

If the prime factorization of a natural number $N$ is $2^4\times 3^4\times 5^3\times 7$, write the number of consecutive zeroes in $N$.

Answer 1

Prime factorization of a natural number $N$ is

$N=2^4\times 3^4\times 5^3\times 7$

The number of consecutive zeroes in $N=Min.(a,b)$

Where, $a,b$ are the exponents of $2,5$ respectively

$\therefore N=Min.(4,3)=3$

Hence, The number of consecutive zeroes in $N=3$