We can ignore all terms not ending in zero. Starting with 10 we form a series with first term 10 and common difference 30, because adding 30 takes us to the next term ending in zero. We can group these for 0-90, 100-190, and so on:
Group Zeroes
10, 40, 70 3
100, 130, 160, 190 5
220, 250, 280 3
310, 340, 370 3
400, 430, 460, 490 5
520, 550, 580 3
610, 640, 670 3
700 2
TOTAL ZEROES: 27
We simply add the number of zeroes together, so there are 27 zeroes at the end of the product.