Finding unit digit - it's all this funda - PaRt-2

Okay!! So you now know how to find the unit digit of a number of the form x^y that ends in 1, 2, 5, 6,.

Before proceeding just see if you can get answers to the below problems

1) 128975^478z

2) 1928321^67846y

3) 8726352^1234

4) 876192736^xyz

Wiyee!! You got all correct than let’s proceed. If you are not sure about any of the above answer than have a look at my post on finding unit digit of a number – Part 1

Now let’s have a look at the number 4 and 9.

Why I selected these two particular numbers?

Just like 1, 5 and 6 these two numbers also have something in common.

Both 4 and 9 have cycles of 2.

4^1 = 4

4^2 =16

4^3 =64

4^4 = 256

Ahh! There you see. Unit digit repeats itself for every two powers. So 4^2k+1 will have 4 as unit digit and 4^2k will have unit digit as 6. To put it in more simple words, 4 raised to even power will have 6 as unit digit and 4 raised to odd power will have 4 as unit digit.

Now if you calculate for 9 it will also yield similar pattern

9^1 = 9

9^2 = 81

9^3 =729

9^4 = 6561

So like you can see 9^x will have unit digit 9 or 1. 9 raised to odd power will have 9 as unit digit and 9 raised to even power will have 1 as unit digit.

So we are done with numbers 1,2,4,5,6 and 9.

Let’s have a look at 3,7 and 8.

What do these numbers have in common?

Just like 2, they have a cycle of 4.

Let’s try 3

3^1 = 3

3^2 = 9

3^3 =27

3^4 = 81

3^5 = 243

Okay! If you can see the unit digit repeating after 3^4, you got the trick.

3^4k+1 will end in 3

3^4k+2 will end in 9

3^4k+3 will end in 7

3^4k will end in 1

Similarly for 7 and 8

7^4k+1 will end in 7

7^4k+2 will end in 9

7^4k+3 will end in 3

7^4k will end in 1

8^4k+1 will end in 8

8^4k+2 will end in 4

8^4k+3 will end in 2

8^4k will end in 6.

There ends my responsibility. Now it’s your turn.

Find out the unit digit for following numbers

1625251^xyz

124352^5416

12735373^267255

1636284^2a

16273835^n

1763826^2n

172637^27635

1738273268^172282

17283639^2b+1

Let me know if you have any questions. My next post will be on permutation and combination.

Happy blogging,

Quant-Master