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

Answer 1

Since, it is given that

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

$$\begin{gathered} =2^3\times 5^4\times 3^4\times 7 \\ =2^3\times 5^3\times 5\times 3^4\times 7 \\ ={\left(2\times 5\right)}^3\times 5\times 3^4\times 7 \\ =5\times 3^4\times 7\times {\left(10\right)}^3 \end{gathered}$$

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