Too large to think!!!
Number Theory
Level
3
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.
3^93
None of these
3^19
3^0
3
3^56
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1 solution
Now first we try to find it is divisible by 3. Its easy as we know that if the sum of the digits is divisible by 3 then the number is also divisible by 3. Noting that 1 occurs 9 times in the digits from 19 to 93, 2 occurs 18 times..etc, we find the sum to be 717. This is divisible by 3 (7+1+7=15) but not by 9. So highest power of 3 dividing N is 3.