Find the number of zeroes in the product of 60 × 61 × 62 × ........ × 80?

Solution

Factors of 5 are 60, 65, 70, 75 and 80 so number of 5 = 6 and number of 2 is very high because every number is followed by even number. Hence, number of zeros = number of 10s = 5 and pair of 2s = 6   Alternate Method : Product = 60 × 61 × 62 × ........ × 80. So we can find number of zeroes in 80! then we can subtract number of zeroes in 59! . So 80/5 = 16 and 16/5 = 3 and adding all quoitent, number of zeroes = 16+3= 19; 59/5 = 11 and 11/5 =2, so number of zeroes in 59! = 11 + 2 = 13. So number of zeroes in the given product = 60 × 61 × 62 × ........ × 80?  = 19 - 13  = 6.