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# Unit Digit Shortcut - Find Last digit of any number

Today I am going to share an interesting technique to solve Unit Digit questions.

Suppose you have a series

P, Q, R, S ,T, P, Q, R, S ,T,P, Q, R, S ,T,P, Q, R, S ,T,P, Q, R, S , T,P, Q, R, S, T .....

And you have to find out the 16th term of the series. How would you do this?

One way to solve this is by counting the 16th term; you get your answer P.

The other way to solve: You can divide the 16 by 5 and get the remainder as 1. So now answer would be the 1st term that is P.

Why we have divided by 5 because the terms in the series are repeated after a cycle of 5.

Let us take another question.

Find out the 25th term of the above series. Following the same procedure you get

25/ 5 gives you the remainder zero (0)

In such case, your answer should be the last term of the cycle and the last term of the cycle is T

25th term is T.

### Find out the unit digit in 268 × 453?

Now to solve this question, you are going to pick up the only last digits and in this case

__ __ 8× _ _ 3 which means 8×3 = 2 4

Unit digit

So the unit digit in the product 268 × 453 is 4.

Remember in such questions, in such questions, you are only going to get concerned about the unit digits

### What is the unit digit in the product 753 × 43 × 1236 × 864?

Solution: let us pick up the unit digits and multiply them

3 in 753

3 in 43

6 in 1236

4 in 864

× 3 × 6 × 4 = ____ 6 (concern only about unit digit in the product)

So the unit digit in the product 753 × 43 × 1236 × 864 is 6.

Now let us observe the pattern in the cycle of different digit in other words after how many cycles the last digit repeats itself.

 2 3 4 5 6 7 8 9 21=2 31=3 41=4 51=5 61=6 71=7 81=8 91=9 22=4 32=9 42=6 52=5 62=6 72=9 82=4 92=1 23=8 33=7 43=4 53=5 63=6 73=3 83=2 93=9 24=6 34=1 44=6 54=5 64=6 74=1 84=6 94=1 25=2 35=3 45=4 55=5 65=6 75=7 85=8 95=9 26=4 36=9 46=6 56=5 66=6 76=9 86=4 96=1 27=8 37=7 47=4 57=5 67=6 77=3 87=8 97=9

From above table we can see that

In case unit digit is 2 or 3 or 7 or 8, it repeats itself after 4 cycles

Now let us pick up some questions based on this observation

### Find the unit digit in 249?

We know in case of 2, it repeats itself after a cycle of 4 . We will divide 49 by 4

49/4 remainder is 1

We write it as

249= 21= 2

That means the unit digit in the 249 is 2.

### Find the unit digit in 352.

Solution: Now here the power is 52 and we know that in case of 3, it repeats itself after a cycle of 4 .

52/4 the remainder is 0.

In such cases, our answer should be the 4th power

So answer is unit digit in 34is 1.

Let us do some more complex examples

### Find the last digit in the 745304000

Solution: In this case we need to divide the power by 4

The power is 45304000

We know that a number is divisible by 4 if the number formed the last two digits is divisible by 4.

00/4 = 0 that means remainder is ZERO and we know that in case of 7 ,the cycle is 4 so we will find out the 4th power of 7

74if you still find difficult, let us simplify it

74= 7× 72

= 9 × 9 (Unit digits)

= 81 Unit digit so the last digit in the 745304000 is 1

From the table we also observe that

in case of 4

If the power is odd, the unit digit is 4 and if the power is even, the unit digit is 6
And same is the case with 9

If the power is odd, the unit digit is 9 and if the power is even, the unit digit is 1

Let us do some of its applications

### Find out the unit digit in 439 × 978 ? In 439 the unit digit is 4 (the power is odd)

In 978 the unit digit is 1 ( the power is even )

The answer is 4 × 1 = 4