Find the number of zeroes at the end of the product of 15 × 25 × 35

Find the number of zeroes at the end of the product of 15 × 25 × 35 × 45 × … × 385.1. 402. 503. 304. 60

Answer» Correct Answer - Option 1 : 40

Given:

The expression is 1⁵ × 2⁵ × 3⁵ × 4⁵ × … × 38⁵

Concept used:

To find the number of zeroes at the end of the product, we need to calculate the number of 2’s and number 5’s or number of pairs of 2 and 5.

2 × 5 = 10 ⇒ Number of zeroes = 1 (number of pair = 1)

The number of pairs of 2 and 5 is same as the number of zeroes at the end of the product

Calculation:

1⁵ × 2⁵ × 3⁵ × 4⁵ × … × 38⁵

In the above expression, number of 2’s is more than the number of 5’s. So we need to calculate the number of 5’s only

Number of 5’s

Total number of 5’s = 5 + 5 + 5 + 5 + 10 + 5 + 5 =40

There are only 40 pairs of 2 and 5 are possible.

∴ The total number of zeroes is 40.