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# 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

2^{4}*2^{4}*2^{4 }= 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**

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

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