Question

What is the remainder when 4444 raised to the power 4444 is divided by 9?

Answer 1

Answer:7

Step-by-step explanation:

To find: Remainder when :

Since, 9 divides 4437, therefore it leaves the remainder of 7 when divided by 4444.

Therefore,

Now, observe a pattern when powers of 7 divides 9.

When 7^1 is divided by 9 it leaves the remainder of 7.

When 7^2 is divided by 9 it leaves the remainder of 4.

When 7^3 is divided by 9 it leaves the remainder of 1.

After 7, 4, 1 the pattern repeats itself.

Now, when 4444 is divided by 3 it leaves the remainder of 1.

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Rahul Sharma

Rahul Sharma, HighSchool Mathematics & Physics and Chemistry, Shri Vaishnav Academy (2000)

Answered Jun 5, 2017 · Author has 98 answers and 74.7k answer views

Originally Answered: What is the remainder when the number 4444^4444 is divided by 9?

Since 4444 ≡ 7 mod 9

44444444 ≡ 74444mod 9

now 73 ≡1 mod 9

so

73∗1481≡11481mod 9

or 74443 ≡ 1 mod9

so 74444mod 9 = 74443∗7mod 9

= 7