All the 2-digit numbers from 19 to 93 are written consecutively to form the number N = 19202122…919293. Find the largest power if 3 that divides N.
a) 30
b) 31
c) 32
d) 33
Ans: b) 31
19 + 20 + 21 + ….. + 93 = (19 + 93)/2 × 75 = 4200 divided by 99 leaves a remainder of 42. ∴ N = 99k + 42 ∴ Largest power of 3 that divides N = 31
