Find the number of zeroes at the end of the product 15!.1. 42. 33. 54.

1.	Find the number of zeroes at the end of the product 15!.1. 42. 33. 54. 2
Answer» Correct Answer - Option 2 : 3 Given: 15! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11 × 12 × 13 × 14 × 15 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: Given expression = 15! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11 × 12 × 13 × 14 × 15 In any factorial value, the number of 5’s is always lesser than the number of 2’s In the above expression, number of 5’s = 3 (5, 10 = 2 × 5, 15 = 3 × 5) Number of 2’s = 11 But total number of pairs of 2’s and 5’s = 3 ∴ The total number of zeroes is 3.

Find the number of zeroes at the end of the product 15!.1. 42. 33. 54. 2

Answer» Correct Answer - Option 2 : 3

Given:

15! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11 × 12 × 13 × 14 × 15

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:

Given expression = 15! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11 × 12 × 13 × 14 × 15

In any factorial value, the number of 5’s is always lesser than the number of 2’s

In the above expression, number of 5’s = 3 (5, 10 = 2 × 5, 15 = 3 × 5)

Number of 2’s = 11

But total number of pairs of 2’s and 5’s = 3

∴ The total number of zeroes is 3.

Discussion

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