Question

Find the unit Digit of 3^123​

Answer 1

Step-by-step explanation:

3 × 3 = 9

3 × 3 × 3 = 27

3 × 3 × 3 × 3 = 81

3 × 3 × 3 × 3 × 3 = 243

Here, in 3⁵ the unit digit is again 3.

So, 3¹²³ = 3 ^ (120 + 3)

( 120 cancelled by 5, so only 3³ remain)

Therefore the unit digit is 3³ unit digit that is 7.

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Answer 2

Answer:

Step-by-step explanation:

The Cyclicity table for 3 is as follows:

3^1 =3

3^2 =9

3^3 = 27

3^4 = 81

3^5 = 243

Let’s divide 123 by 4 and the remainder is 3.

Thus, the last digit of 3^123 is equal to the last digit of 3^3 i.e. 7.