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