NMOS 2010 Q12

Q12. We define the ending zeroes of an integer as the number of zeroes at the end of the integer. For example, 2010 has one ending zero whereas 10010000 has four ending zeroes. How many ending zeroes are there when the value of 16x17x18x…..x209x210 is simplified?


25, 75, 175  = ..00 --> 2 x 3 = 6


125 = ..000  --> 3

35, 45, 55, 65, 85, 95, 105, 115, 135, 145, 155, 165, 185, 195, 205 --> 15


50, 150 = ..00 --> 2 x 2 = 4

100, 200 --> 2 x 2 = 4


20, 30, 40, 60, 70, 80, 90, 110, 120, 130, 140, 160, 170, 180, 190, 210 --> 16



6 + 3 +  15 + 4 + 4 + 16 = 48 zeros