Discussion

How many trailing zeros are there in the product \(20 \times 25 \times 30 \times 35 \times 40\)?

Answer: B

Correct answer: 6

Each trailing zero comes from a factor of 10, that is a pair of 2 and 5, so count both primes across the product.

\[20 = 2^2\times 5,\quad 25 = 5^2,\quad 30 = 2\times 3\times 5,\quad 35 = 5\times 7,\quad 40 = 2^3\times 5\]

Fives: \(1 + 2 + 1 + 1 + 1 = 6\). Twos: \(2 + 0 + 1 + 0 + 3 = 6\).

The number of zeros is the smaller count, so 6. Multiplying out confirms it: the product is 21000000.

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