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Find the number of zeroes at the end of the product of 15 × 25 × 35 × 45 × … × 385.
1. 40
2. 50
3. 30
4. 60

1 Answer

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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

 

 

No. of 5

55

(1 × 5)5

5

105

(2 × 5)5

5

155

(3 × 5)5

5

205

(4 × 5)5

5

255

(5 × 5)5

10

305

(6 × 5)5

5

355

(7 × 5)5

5

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.

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