Question

Find the number of zeros at end of 5 × 10 × 15 × 20 × …x 100.

1. 10
2. 20
3. 18
4. 24

Answer 1

Correct Answer - Option 3 : 18

Given:

5 × 10 × 15 × 20 × …x 100

Concept Used:

Number of zeros = Number of pairs of 2 × 5

n! = n(n – 1)(n – 2)…1

Maximum power of 5 in n! = n/5 + n/5² + n/5³ +... (Consider integer values only)
Maximum power of 2 in n! = n/2 + n/2² + n/2³ +... (Consider integer values only)

Calculation:

Number of 5 in 5, 10 … 100 = 100/5 = 20 (Consider integer values only)

The given expression 5 × 10 × 15 × 20 × … × 100

⇒ 5²⁰(1 × 2 × 3 × 4 × … × 20)

⇒ 5²⁰ × 20!

Power of 5 in 20! = 20/5 = 4

Power of 2 in 20! = 20/2 + 20/2² + 20/2³ + 20/2⁴   = 10 + 5 + 2 + 1 = 18

In the given expression 5²⁰ × 20! maximum power of 5 is 24 and maximum power of 2 is 18. So, there are 18 pairs of 2 × 5.

∴ The number of zeros is 18.