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 × 978In 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
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10 comments:

  1. Thank you sir...

    ReplyDelete
  2. Sir please provide some topics important for the BOB manipal gd ....

    ReplyDelete
  3. 7th & 8th rows need a change!

    ReplyDelete
  4. in the given table., do correct the columns of 7 and 8... 7^1 wil have 7 and not 9 and similarly 8^1 wil hav 8 and not 4 and simmilarly the entire column..

    ReplyDelete
  5. check this - http://www.bankexamstoday.com/2015/05/gd-topics-for-bank-of-baroda-po-program.html

    ReplyDelete

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