Question

The number of consecutive zeros in \[2^3    \times  3^4    \times  5^4    \times 7\] is

Options

• 3

• 2

• 4

• 5

Answer 1

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

\[2^3 \times 3^4 \times 5^4 \times 7 = 2^3 \times 5^4 \times 3^4 \times 7\]

\[ = 2^3 \times 5^3 \times 5 \times 3^4 \times 7\]

\[ = \left( 2 \times 5 \right)^3 \times 5 \times 3^4 \times 7\]

\[ = {10}^3 \times 5 \times 3^4 \times 7\]

\[ = 5 \times 81 \times 7 \times 1000\]

\[ = 2835000\] 

Therefore the consecutive zeros at the last is 3