Find the number of zeroes at the end of the product of 5 × 10 × 15 �

1.	Find the number of zeroes at the end of the product of 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50. 1. 122. 63. 84. 9
Answer» Correct Answer - Option 3 : 8 Given: Expression is 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 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: 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 ⇒ 5¹⁰(1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10) ⇒ 5¹⁰(1 × 2 × 3 × 2 × 2 × 5 × 2 × 3 × 7 × 2 × 2 × 2 × 9 × 2 × 5) ⇒ 5¹²(1 × 2 × 3 × 2 × 2 × 2 × 3 × 7 × 2 × 2 × 2 × 9 × 2) ⇒ 5¹² × 2⁸ × 3² × 7 × 3² There are only 8 pairs of 2 and 5 are possible ∴ The total number of zeroes at the end of the product is 8.

Find the number of zeroes at the end of the product of 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50. 1. 122. 63. 84. 9

Answer» Correct Answer - Option 3 : 8

Given:

Expression is 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50

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:

5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50

⇒ 5¹⁰(1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10)

⇒ 5¹⁰(1 × 2 × 3 × 2 × 2 × 5 × 2 × 3 × 7 × 2 × 2 × 2 × 9 × 2 × 5)

⇒ 5¹²(1 × 2 × 3 × 2 × 2 × 2 × 3 × 7 × 2 × 2 × 2 × 9 × 2)

⇒ 5¹² × 2⁸ × 3² × 7 × 3²

There are only 8 pairs of 2 and 5 are possible

∴ The total number of zeroes at the end of the product is 8.