Question

How many zeroes are there at the end of the following product?

1 × 5 × 10 × 15 × 20 × 30 × 35 × 40 × 45 × 50 × 55 × 60 

1. 10
2. 12
3. 14
4. 15

Answer 1

Correct Answer - Option 1 : 10

Given:

1 × 5 × 10 × 15 × 20 × 30 × 35 × 40 × 45 × 50 × 55 × 60 

Concept used:

To get a zero we need 5 × 2

Calculation:

We need find the number of 2's and 5's

⇒ 1 × 5 × 10 × 15 × 20 × 30 × 35 × 40 × 45 × 50 × 55 × 60 

⇒ 1 × 5¹ × 1 ×  5¹ × 2¹ × 1 ×  5¹ × 2² × 5¹ × 5¹ × 5¹ × 2¹ × 10⁶

⇒ 2⁴ × 5⁶ × 10⁶

There are only 4 2's and 6 5's. 

We need both 2 and 5 to get a 0

So, only 4 new zeros added to 6

Number of zeros = 4 + 6 = 10

∴ There will 10 number of zeros.