Discussion
Find the number of trailing zeros in the expression \(100! + 200!\)
Answer: A
Let N1 = 100! and N2 = 200!. When adding numbers, the number of trailing zeros in the sum is determined by the number with the fewer trailing zeros. We can factor out the smaller number of zeros. For example, \(100 + 1000 = 100(1+10) = 1100\). The number of zeros is 2, same as in 100. So we need to find the number of zeros in 100!. Number of zeros in 100! = \(\lfloor 100/5 \rfloor + \lfloor 100/25 \rfloor = 20 + 4 = 24\). Number of zeros in 200! is \(40+8+1=49\). The smaller number is 24, so the sum will have 24 trailing zeros.
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