If the prime factorization of a natural number n is

Question:

If the prime factorization of a natural number n is 23 ✕ 32 ✕ 52 ✕ 7, write the number of consecutive zeros in n.

Solution:

Since, it is given that 

$n=2^{3} \times 3^{2} \times 5^{2} \times 7$

$n=8 \times 9 \times 25 \times 7$

n=(7 \times 9 \times 2) \times(4 \times 25)

$n=(7 \times 9 \times 2) \times 100$

$n=(7 \times 9 \times 2) \times 100$

$n=12600$

Hence the number of consecutive zeroes are2

 

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