# The number of consecutive zeros in

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

Solution:

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

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

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

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

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

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

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

$=5 \times 81 \times 7 \times 1000$

$=2835000$

Therefore the consecutive zeros at the last is 3

So the option (a) is correct