Since 10 = 2 * 5, we need to count the number of factors of 2 and 5 in the product. There will always be more factors of 2 than 5, so we only need to count the factors of 5.
In the numbers from 1 to 50, there are 10 multiples of 5 (5, 10, 15, ..., 50). However,
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