Question

what is the number of zeros at the end of the product 5^5×10^10×15^15×.....×125^125​

Answer 1

We only have to consider the powers of multiplies of 10 in this product.

In this product, powers of multiplies of 10 like 10^10, 20^20, 30^30 upto 120^120 are multiplied.

Well,

→ 10^10 ends in 10 zeros.

→ 20^20 ends in 20 zeros.

→ 30^30 ends in 30 zeros.

Likewise, to 120^120,

→ 120^120 ends in 120 zeros.

Hence total no. of zeros will be,

10 + 20 + 30 + ...... + 120

=> 10(1 + 2 + 3 + ...... + 12)

=> (10 × 12 × 13) / 2

=> 780