What is the greatest integer, k, such that 5^k is a factor of the product of the integers from 1 through 24, inclusive?

Answer: k = 4

Step-by-step explanation: greatest k, which 5^k is a factor of

the product of the integers from 1 through 24

From 1.2.3 ... 24, if we factor all these numbers to prime integers, we can find 5 in: 5, 10, 15 and 20.

5; 2.5; 3.5; 4.5, so 5^4 is a factor of this product.

This way, k = 4