Question
The number of consecutive zeroes in \(2^3 \times 3^4 \times 5^4 \times 7\) is:
(a) 3
(b) 2
(c) 4
(d) 5
Solution
Trailing zeros are formed by factors of \(10 = 2 \times 5\).
Count the number of 2s and 5s:
\[ 2^3 \Rightarrow 3 \text{ factors of 2} \]
\[ 5^4 \Rightarrow 4 \text{ factors of 5} \]
Number of zeros = minimum of (3, 4)
\[ = 3 \]
Other factors \(3^4\) and \(7\) do not affect zeros.
Final Answer
✔ Correct option: (a) 3