First 50 multiples of 20 i.e, 20, 40, 60, ……., 1000 are multiplied together. How many numbers of zeroes are there at the end of the product?

The number of zeroes at the end of a product is determined by the number of times 10 is a factor in that product. 10 is the product of 2 and 5, so we need to count the number of times 2 and 5 are factors in the product.

In this case, we are multiplying the first 50 multiples of 20. Each of these multiples is even, so there are at least 50 factors of 2. Each multiple of 20 is also a multiple of 5, so there are also 50 factors of 5.

Therefore, there are at least 50 factors of 10 in the product, which means there are at least 50 zeroes at the end of the product. However, some multiples of 20 are also multiples of 100 (205, 2010, 2015, etc.), which means they contribute an extra factor of 10. There are 10 such multiples in the first 50 multiples of 20 (205, 2010, ..., 2050), so they contribute an extra 10 factors of 10.

So, the total number of zeroes at the end of the product is 50 (from the multiples of 20) + 10 (from the multiples of 100) = 60.