What is the largest positive integer n for which 3^n divides 44^44? Answers.
A) 0
B) 9
C) 8
D) 7
E) 6
The digit sum of 44444444 is when remainder obtained 44444444 divided by 9   44444444 = (45−1)44(45−1)44   Each term is a multiple of 9 but the last term which is (−1)44(−1)44 = 1   So the digit sum of 44444444 is 1.   Now the divisibility rule for 3, 9, 27... is the sum of the digits should be divisible by 3, 9, 27 respectively. In each case the digit sum is either multiple of 3 or 9.   So for any value of n &gt; 1, the given expression is not divisible by 3n   0nswer:	0
<result>A</result>
What is the largest positive integer n for which 3^n divides 44^44?