Q. How many zeroes are there at the end of the following product?
1 x 5 x 10 x 15 x 20 x 25 x 30 x 35 x 40 x 45 x 50 x 55 x 60
(a) 10
(b) 12
(c) 14
(d) 15
Correct Answer: (a) 10
Question from UPSC Prelims 2020 CSAT Paper
Explanation :
Number of zeroes at the end of product
1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60
= 1 × 5 × (5 × 2) × (5 × 3) × (5 × 2^2) × (5 × 5) × (5 × 3 × 2) × (5 × 7) × (5 × 2^3) × (5 × 9) × (5 × 5 × 2) × (5 × 11) × (5 × 2^2 × 3)
Here, number of 2s = 10
And number of 5s = 14
The lesser of the two will determine the number of zeros.
Hence, there will be 10 zeros at the end in the given expression.
