# Tips Tricks and Shortcuts for Divisibility

## Tips Tricks And Shortcuts on Divisibility

The process of whether the given number is exactly divisible by another number without actually performing the operation of division is called the test of divisibility. ### Tips and Tricks  and Shortcuts for Divisibility

The divisibility rule is the shorthand method of determining whether a number divisible by fixed divisor.

• Rule for 2
The number on divisible for 2 when the number is ending with 2,4,6,8.

• Rule for 3
If the sum of digit is divisible by 3 than the number is divisible by 3.

• Rule for 4
If the last two digit is divisible by 4, than the number is divisible by 4.

• Rule for 5
Number is divisible by 5 if the last digit is 0 or 5.

• Rule for 6
A number is divisible by if number is divisible by 2 AND 3.

• Rule for 7 : Double the last digit and subtract it from the remaining leading truncated number to check if the result is divisible by 7 until no further division is possible

• Rule for 8
If the last 3 number is divisible by 8 than the number is divisible by 8.

• Rule for 9
Same as divisibility of 3.

• Rule for 10
If the last digit is 0 than the number is divisible by 10.

### Type 1:Find the largest or smallest number

Question 1.Find the smallest 4 digit number which is exactly divisible by 41?

Options.

A. 1000

B. 1023

C. 1025

D. 1012

Solution      Smallest 4 digit number is 1000

On dividing 1000 by 41, remainder = 16

Required number = 1000 + (41 – 16) = 1025

Correct option: 3

### Type 2:Which of the following numbers is/or not divisible by given number.

Question 1. Which of these numbers is divisible by 3?

Options.

A. 1003

B.  253

C. 1031

D. 1221

Solution      Solution: 1003 = 1 + 0 + 0 + 3 = 4, 4 is not divisible by 3

253 = 2 + 5 + 3 = 10, 10 is not divisible by 3

1031 = 1 + 0 + 3 + 1 = 5, 5 is not divisible by 3

1221 = 1 +2 + 2 + 1= 6, 6 is divisible by 3

Correct option: 4

### Type 3: Tips and Tricks to Solve Divisibility Questions.Find the remainder

Question 1. Find out the remainder of $\frac{2^{12}}{5}$

Options.

A. 1

B. 2

C. 0

D. 3

Solution     Convert the base in power

24*24*2= 16 * 16 * 16

Now divide each number by 5

On dividing 16 by 5 we get remainder as 1

Now, multiply all the remainders 1 * 1 * 1 = 1

Read Also How to solve divisibility questions

### 7 comments on “Tips Tricks and Shortcuts for Divisibility”

• Subhransu Surya

In Type 1:Find the largest or smallest number, if it ask for largest how to proceed 0
• Subhransu Surya

I got it. 2
• PrepInsta

Contact the mentors on our telegram support group where teachers will answer you accordingly. 1
• Gudla

where we can find mock tests 4
• HelpPrepInsta

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• Anwesh

Help me out in the last question? I don’t understand 3
• HelpPrepInsta

Hello Anwesh, 2