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CSAT 2024

Q9 2024, Number System

We need to find the number of consecutive zeros at the end of the integer obtained by multiplying certain numbers together.
Zeros occur when a factor of 5 pairs with a factor of 2. Hence, to find the number of zeros at the end of the product, we need to focus on the factors of 5 and 2 in each term of the product.
Since, in this progression, factors of 2 are more common than factors of 5, we should count the number of factors of 5.
In the given sequence, we observe that the power of 5 increases every fifth term:
5¹⁰ x 10²⁰ x 15³⁰ x 20⁴⁰ x 25⁵⁰.
Factoring it: 10 = 5 *2, 20 = 5*2*2, 25 = 5*5.
Total 5s in the sequence: 5¹⁰x 5²⁰x 15³⁰x 5⁴⁰x 5¹⁰⁰.
Hence, the sum of these powers is 200.