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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