## In this article, you are going to learn how to find unit place digit of complex multiplication mentally and quickly without actually finding the complete product.

Lets take an example:

456*35467*2345829* 483457*12

Remember This: The unit place digit in the product will depend on unit place digit of each individual numbers in the expression of the form A*B*C*D*E…where A,B,C,D,E are any positive integers.We can neglect rest of the digits and find the product, the unit place digit will remain the same.

Taking unit place digits of each number:

6*7*9*7*2

In next steps we can again neglect tenth and higher place digits.

6*7=42 take it as 2

2*9=18 take it as 8

so the product will become

8*7*2

again 8*7= 56 take it as  6

Now the product is 2*6

2*6=12 take it as 2, hence 2 is the unit place digit of the product 456*35467*2345829* 483457*12.

Oh yes ! By the way I have calculated the product by calculator to give you feel how difficult it would be to find the product first and then to say that 2 is the unit place digit even if you are answering by using calculator.

456*35467*2345829* 483457*12= 220102384385855136672

Now I’m going to tell you how can you use this method to save  your time in exams.You are going to love it.Don’t miss it.

Suppose ,if you are solving data interpretation objective problem or at the end of any problem you find that you need to find difficult multiplication to get to the answer. You see your watch, and say Oh ! my God, I don’t have enough time left,this will kill my time,lets move on to other problem…Then don’t do this again.

Here is your time saving trick for that situation,if  there are four options and you need to choose only one correct option and all the four options has different unit place digit then choose one having unit place digit as 2 for the above product..

For example solve this  below problem within 30 seconds only one option is correct.

345*67*45*634*12*23

(a)182013982200 (b))182013982101 (c))182013982232 (d) )182013982355

You can now quickly find unit place digit ZERO  of the product by the method described by me.You can easily choose option (a) here. As only option (a) has unit place digit as zero and other options don’t have unit place digit as zero.

Quick calculation tips:

1.If any number in the expression A*B*C*D… has zero as unit place digit then we will certainly get zero as unit place digit in product too.

2. If in the expression A*B*C*D…  If any number has 5 as unit place digit and if there is  even one Even number present in the expression then unit place digit in the product will be zero.Like in the example above.

3.Finding unit place digit of the expression A*B*C*D….  is the same as finding remainder when expression will be divided by 10.

Now try to solve the below objective problem.

12*437*678*546*6537

(a) 12690055005264  (b)12690055005274   (C) 12690055005273   (D) 12690055005263

You can easily find unit place digit as 4, option (A) or option (B) can be the correct choice.

In option (A) and option (B) tenth place digit is 6 and 7 respectively ,so finding the tenth place digit will let us know the correct option.I will soon publish method to find tenth place digit of any multiplication easily.

Niraj Tulsyan

Btech in Electronics & Communication.I love Maths, Science & Technology.

### 8 replies to "How to find unit digit in multiplication quickly."

• Diana

How do you find the 10th unit, then? D:

• bappan dass

how to find the area of irregular polygon

• Chandini

Plz can u provide all topics of aptitude easy methods to solve problems with in seconds

• Dharmik

Thank you sir
This helps me a lot.