Finding unit digit - it's all this funda - PaRt-1

I was heading to post “How to find the last two digit of a number that appears in weird form say 37^234566” then I realized I am yet to post “How to find unit digit of a number”!! So stupid of me:D

Okay! Let’s get on with the business:

First let me ask you few questions. If I ask you to find unit digit of the below mentioned numbers, how comfortable you are?

31^167535

6756425^243538

200019182^266435483

Very comfortable

Comfortable

Not that comfortable

Not comfortable at all

If you selected any of the last two options then read on!!

Well, for all the three questions I posted above I just typed the numbers as my finger went. I never bothered what number I am typing. Know why? Because no matter what the number is we approach it in very much the same way.

Let’s get on with the work now!!

All the numbers have its cycles. You should know that to proceed further

If we take the number 1: 1 raised to any power will have unit digit 1. This also holds true for any number that ends in 1. Example 41^x, 5011^x, 611^x etc will have unit digit as 1.

Now you have the answer for the first question I posted. Unit digit of 31^167535 ??

It’s 1 of course.

Same property applies for 0, 5 and 6. Any number that ends in 0, 5 or 6 will have same unit digit.

What if I get any other number which is not mentioned above? How do I find unit digit?

Here it is how:

Let’s take the cycles of each number and try to analyze them

Let’s take 2 :

2^1 is 2

2^2 is 4

2^3 is 8

2^4 is 16

2^5 is 32

2^6 is 64

Now if you notice the unit digit is repeating after the power 4. So the cycle of 2 is 2, 4, 8, 6.

Hence cycle can be expressed in 4k form. Why should I take it in 4k form? Here is why

Find the unit digit of 2^1676.

1676 is a multiple of 4. Hence 1676 can be expressed as 4k. Therefore 2^4k will have unit digit as 6.

Let’s take another example 132^1233.

Forget how big the number is. Just consider 2^1233. 1233 when divided by 4 will give a remainder of 1. Hence it is of the form 4k+1. When the number is of the form 4k+1 it means a cycle of 4 is complete and hence the first number of the cycle will be its unit digit which is 2.

Now you should have answers to all my questions posted above

Try these numbers and post the answer using comment option

Find the unit digit of

1230^56909374

122255^3279495763

7865436^129084645

1232^1201

18972^1223

9874562^1782

Once you are clear with this, based on your response, I will post the approach to find unit digit of numbers ending in 3,4,7,8 and 9.

Thanks,

Quant-Master