Let M represent the product of all integers from 1 to 80, inclusive. How can we determine the maximum integer value of L such that 10^L is a factor of M?

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Official Explanation

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M is the product of all integers from 1 to 80, inclusive. To find the highest power of 10 that divides M, we note that 10 can be expressed as 2 multiplied by 5. Since there will always be more factors of 2 than…

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Comments

LauraFeb 11, 2025

thanks a lot

SamyukthaApr 25, 2024

thank you very much!

What this question tests

What it tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Common trap

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).