Question

If n = 2³ ✕ 3⁴ ✕ 5⁴ ✕ 7, then the number of consecutive zeros in n, where n is a natural number, is

Options

• 2

• 3

• 4

• 7

Answer 1

Since, it is given that 

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

\[= 2^3 \times 5^4 \times 3^4 \times 7\]
\[ = 2^3 \times 5^3 \times 5 \times 3^4 \times 7\]
\[ = \left( 2 \times 5 \right)^3 \times 5 \times 3^4 \times 7\]
\[ = 5 \times 3^4 \times 7 \times \left( 10 \right)^3\]

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