Question

What is the remainder when the number (4444)^4444 is divided by 9?
(a) 4
(6) 6
(C) 7
(d) 8
[CDS (I) Exam, 2017]​

Answer 1

Step-by-step explanation:

What will be the remainder of (4444)44449 ?

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Remainder is 7.|

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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