Maths tricks - square and multiplication tricks

Learn shortcut tricks of math for competitive exams. Math tricks like square tricks, multiplication tricks and LCM tricks are defined beautifully.

I guarantee these maths tricks and shortcuts will blow your mind and they will help in your competitive exams to calculate with lightening speed.

1) Square trick  

Square of a two-digit number close to 50

Case 1: If the number is greater than 50.

For example, let’s take the number 54.

Step 1: Write the 54 as addition of two numbers but one number must be 50

54 can be written as (50+4)

Step 2: Here  4 is added on 50. Hence 4 square = 16 forms the digits at the extreme right.

Step 3: Add 4 in 25 it comes out 29. So, they form the remaining digits.

So, the square of 54 is equal to 2916.

Square tricks

Case 2: If the number is lesser than 50.

For example, let’s take the number 46

Step 1: 46 can be written as (50-4)

Step 2: Here  4 is subtracted from 50. Hence 4 square = 16 forms the digits at the extreme right.

Step 3: Here subtracted number was 4, so subtract 4 from 25 it comes out 21. So, they form the remaining digits

So, the square of 46  is equal to 2116

Square tricks 

Let’s take one more example that is 37

Tricks for square in maths

2) Multiplying 2 numbers ranges from 90 to 100.

Example: 95*96

Multiplication tricks

3) Multiply a number to another number having only 9 as the digit

Example: 999 * 232

Step 1: Subtract "1' from 232

              232 - 1 = 231

Step 2:  Subtract 232 from 999

              999 - 231 = 768

So answer of 999 * 232 is 231768.

4) Find the square of a number having 5 as unit digit

Example: Let's take 65

square trick math 

5) LCM trick ( How to find LCM in mind )

Find the LCM of 2, 4, 6, 8 10, and 12

Step 1: Identify the largest number among the given number

             

Step 2: Check whether the largest number is divisible by all other numbers, if it is divisible by all other numbers the largest number itself will be the LCM otherwise double the largest number and again check whether the number coming from doubling the largest number is divisible by all the numbers, if it is divisible by all other numbers that number will be the LCM otherwise triple the largest number and so on. 

From step 1: Among 2, 4, 6, 8, 10, and 12 we know 12 is the largest number.

From step 2: 12 is not divisible by 8, 10.

12*2 = 24 , again 24 is not divisible by 10

12*3 = 36, again 36 is not divisible by 10

12*4 = 48, again 48 is not divisible by 10

12*5 = 60, again 60 is not divisible by 10

12*6 = 72, again 72 is not divisible by 10

12*7 = 84, again 84 is not divisible by 10

12*8 = 96, again 96 is not divisible by 10

12*9 = 108, again 108 is not divisible by 10

12*10 = 120, 120 is divisible by 10

So, 120 is the LCM of  2, 4, 6, 8, 10, and 12

Know LCM and HCF In detail

6) Find the total no. of the squares in a rectangle of side m*n =

Total no. of the squares in a rectangle of side m*n =
m*n + (m-1)*(n-1) + (m-2)* (n-2) + …………( stop when m or n become zero)

Example: Find the total no. of squares in a rectangle of 5*4

Total no of the squares in the 5*4 rectangle = (5*4) + (4*3) + (3*2) + (2*1)

 = 20 + 12 + 6 + 2 = 40

7) Find the total no of the squares in a square

Total no of square in a square of n*n = n square + (n-1) square + (n-2) square + ……………

 Example: find the total no. of the squares in a square of 5*5

  

 Total no. of square in a square of 5*5 = (5*5) + (4*4) + (3*3) + ( 2*2) + (1*1)
= 25 + 16 + 9 + 4 + 1 = 55

Know in depth to calculate total number of square and total number of rectangles 

8) Find the number of rectangles in a rectangle of m*n

Number of rectangles in a rectangle of m*n = [m*(m+1)/2] * [n*(n+1)/2] 

Example: find the total no. of the rectangle in a rectangle of 5*6

                      

Solution:

Total no. of rectangle in a rectangle of 5*6 = [5* (5+1)/2] * [6*(6+1)/2]

= [5*6/2] * [ 6*7/2]
= 15 * 21 = 315

4  

9) Find the number of rectangles in a square

Number of rectangles in a square of side length ‘n’ = [n*(n+1)/2] square   

 

Example: find the total no. of rectangles in a square having side length equal to 5.

Solution: [5*(5+1)/2] square = [5*6/2] square =
= 15 square = 125.

10) Quick way to know whether a number is divisible by a certain number

A number is divisible by-

• 10, if the number ends in 0
• 9. when the digits are added together and the total sum is divisible by 9
• 8, if the last three digits are divisible by 8 or are 000
• 6, if it is an even number and when the digits are added together the sum of digits is divisible by 3
• 5, if the number ends with 0 or 5
• 4, if it ends in 00 or if its last two digits are divisible by 4
• 3,when the digits are added together and the result is evenly divisible by the number 3
• 2, if it ends in 0, 2, 4, 6, or 8

11) Find the unit digit of a number raised to a power

This tricks is very important for competition exams many time question is directly asked related to unit digit. 

Before jumping to the trick let's know a basic thing that If a number is written in the form of  X raised to power Y, here  X is base whose unit digit may vary from 0 to 9 and Y is exponent whose unit digit also may vary from 0 to 9.

CASE 1: Base has a unit digit equal to 1

If the base has 1 in its unit place on raising its power to any number there will be always 1 in unit place of the answer, no matter what the exponent is.

Example: find the unit digit of 3161 raised to power 24

Here the base is 3161 and its unit digit is 1

Hence unit digit in the answer will be 1.

CASE 2: If the base has a unit digit equal to 2.

• If on dividing the exponent by 4  if we get a remainder equal to 1 it means there will be 2 in unit place in the answer.
• If on dividing the exponent by 4  if we get a remainder equal to 2 it means there will be 4 in unit place in the answer.
• If on dividing the exponent by 4 if we get a remainder equal to 3 it means there will be 8 in unit place in the answer.
•  If on dividing the exponent by 4  if we get a remainder equal to 0 it means there will be 6 in unit place in the answer. 

Example: Find the unit digit of 152 raised to power 343

Here the base is 152 and the unit digit of Base is 2. So only four numbers are possible at the unit place and those are 2, 4, 8 and 6.

Now, focus on the only exponent and that is 343.

On Dividing 343 by 4, we get the remainder equal to 3. So, there will be 8 at the unit place.

CASE 3: Base has unit digit equal to 3..

• On dividing the exponent by 4 if we get a remainder equal to 1 it means there will be 3 in unit place in the answer.
• On dividing the exponent by 4 if we get a remainder equal to 2 it means there will be 9 in unit place in the answer.
• On dividing the exponent by 4 if we get a remainder equal to 3 it means there will be 7 in unit place in the answer.
• On dividing the exponent by 4 if we get a remainder equal to 0 it means there will be 1 in unit place in the answer.

Example: find unit digit of 323 raised to power 133

Here the base is 323 and its unit digit is 3 and the exponent is 133

On dividing the 133 by 4 we get a remainder equal to 1.

Hence unit digit in the answer will be 3.

CASE 4: Base has a unit digit equal to 4.

• On dividing the exponent by 2 if we get a remainder equal to 1 it means there will be 4 in unit place in the answer.
• On dividing the exponent by 4 if we get a remainder equal to 0 it means there will be 6 in unit place in the answer.

Example: find the unit digit of 414 raised to power 34

Here the base is 414 and it is unit digit is 3 and exponent is 34.

On dividing 34 by 2 we get a remainder equal to 0.

Hence unit digit in the answer will be 6.

CASE 5: Base has a unit digit equal to 5.

If the base has 5 in its unit place on raising its power to any number there will be always 5 in unit place of the answer, no matter what the exponent is.

Example: find the unit digit of 4155 raised to power 567

Here the base is 4155 and its unit digit is 5

Hence unit digit in the answer will be 5.

CASE 6: Base has a unit digit equal to 6.

If the base has 6 in its unit place on raising its power to any number there will be 6 in unit place of the answer, no matter what the exponent is.

Example: find the unit digit of 316 raised to power 24

Here the base is 316 and its unit digit is 6

Hence unit digit in the answer will be 6.

know in-depth to solve unit digit questions

CASE 7: Base has unit digit equal to 7

• On dividing the exponent by 4 if we get a remainder equal to 1 it means there will be 7 in unit place in the answer.
• On dividing the exponent by 4 if we get a remainder equal to 2 it means there will be 9 in unit place in the answer.
• On dividing the exponent by 4 if we get a remainder equal to 3 it means there will be 3 in unit place in the answer.
• On dividing the exponent by 4 if we get a remainder equal to 0 it means there will be 1 in unit place in the answer.

Example: find unit digit of 3237 raised to power 133

Here the base is 323 and its unit digit is 3 and the exponent is 133

On dividing 133 by 4 we get a remainder equal to 1.

Hence unit digit in the answer will be 7.

CASE 8: Base has unit digit equal to 8.

• On dividing the exponent by 4 if we get a remainder equal to 1 it means there will be 8 in unit place in the answer.
• On dividing the exponent by 4 if we get a remainder equal to 2 it means there will be 4 in unit place in the answer.
• On dividing the exponent by 4 if we get a remainder equal to 3 it means there will be 2 in unit place in the answer.
• On dividing the exponent by 4 if we get a remainder equal to 0 it means there will be 6 in unit place in the answer.

Example: find unit digit of 36838 raised to power 232

Here the base is 36838 and its unit digit is 8 and the exponent is 232

On dividing 232 by 4 we get a remainder equal to 0.

Hence unit digit in the answer will be 6.

CASE 9: Base has a unit digit equal to 9

• On dividing the exponent by 2 if we get a remainder equal to 1 it means there will be 9 in unit place in the answer
• On dividing the exponent by 2 if we get a remainder equal to 0 it means there will be 1 in unit place in the answer.

Example: find the unit digit of 889 raised to power 889

Here the base is 889 and its unit digit is 9 and exponent is 889.

On dividing 889 by 2 we get a remainder equal to 1.

Hence unit digit in the answer will be 9.

CASE 10: Base has a unit digit equal to 0.

It means if the base has 0 in its unit place on raising its power to any number there will be always 0 in the unit place of the answer, no matter what the exponent is.

Example: find the unit digit of 3120 raised to power 24

Here the base is 3120 and its unit digit is 0

Hence unit digit in the answer will be 0.

Dear readers, Please provide your feedback about this post in comments section. If you have any queries you can ask in comment section, I am always there for you.

Also, Please like, share and follow my blog.