How many zeroes are there in the product of 1 × 2 × 3 × 4 ......49 × 50 :

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Solution

Each multiple of 5 - taken together with some even number - contributes a multiple of 10 which have zero.
On counting we find there are 10 multiples of 5 (5, 10, 15, 20, 25, 30, 35, 40, 45, 50).

Again each multiple of 25, however - taken together with some even number - contributes two multiples of 10 which h.ave zeroes
Thus there are 2 multiples of 25 in the product 1 to 50 (25 and 50)

Thus, there are a total of 10+2 =12 zeros in the given product.

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