How many zeros does the product $5\times 10\times 15\times 20$ × … × 50 end with?

Take a 5 out of each of the ten factors: the product is $5^{10}\times (1\times 2$ × … × 10) = $5^{10}\times 10$!. Now 10! = $2^8\times 3^4\times 5^2\times 7$, so altogether there are 10 + 2 = 12 factors of 5 but only 8 factors of 2. Each zero needs a 2 and a 5, so the number of zeros is the smaller count, 8.