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KCET 2004 Math Solved Paper

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Question : 2 of 60

Marks: +1, -0

The last digit in

7^{300}

7
9
1
3

Solution:

The last digits of powers of

7

repeat in a cycle of length

4

:

7^1

ends in

7

,

7^2

ends in

9

,

7^3

ends in

3

, and

7^4

ends in

1

.

Since

300 = 4 \times 75

, we have

300 \equiv 0 \pmod{4}

.

So

7^{300}

has the same last digit as

7^4

.

Therefore, the last digit of

7^{300}

is

1

.

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