If n
Question:

If n = 23 ✕ 34 ✕ 54 ✕ 7, then the number of consecutive zeros in n, where n is a natural number, is

(a) 2

(b) 3

(c) 4

(d) 7

Solution:

Since, it is given that 

$n=2^{3} \times 3^{4} \times 5^{4} \times 7$

$=2^{3} \times 5^{4} \times 3^{4} \times 7$

$=2^{3} \times 5^{3} \times 5 \times 3^{4} \times 7$

$=(2 \times 5)^{3} \times 5 \times 3^{4} \times 7$

$=5 \times 3^{4} \times 7 \times(10)^{3}$

So, this means the given number n will end with 3 consecutive zeroes.

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