SCRATCH YOUR HEAD !!!
All the 2-digit numbers from 19 to 93 are written consecutively to form the number N = 19202122...919293 . Find the largest power of 3 that divides N .
The answer is 3.
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1 solution
To test the divisibility of the number N = 19202122...919293 by 3 or 9 we should find the sum of the digits of N . Nothing that 1 occurs 9 times in the digits from 19 to 93 (in 19 19, 21, 31, ..., 91) , 2 occurs 18 times (in 20, 21, 22, ..., 29, 32, 42, ..., 92) etc. We find the sum of the digits of N to be 717 . This number is divisible by 3(since 7 + 1 + 7 = 15 is so) but not by 9 . Thus the highest power of 3 dividing N is 3 .