Question

The number of consecutive zeros in $2^3\times 3^4\times 5^4\times 7$, is

(a) 3

(b) 2

(c) 4

(d) 5

Answer 1

We are given the following expression and asked to find out the number of consecutive zeros

We basically, will focus on the powers of 2 and 5 because the multiplication of these two number gives one zero. So

$$\begin{gathered} 2^3\times 3^4\times 5^4\times 7=2^3\times 5^4\times 3^4\times 7 \\ =2^3\times 5^3\times 5\times 3^4\times 7 \\ ={\left(2\times 5\right)}^3\times 5\times 3^4\times 7 \\ ={10}^3\times 5\times 3^4\times 7 \\ =5\times 81\times 7\times 1000 \\ =2835000 \end{gathered}$$

Therefore the consecutive zeros at the last is 3

So the option (a) is correct