How To Check If A Register Is Devisable

Divisibility rules or Divisibility tests have been mentioned to make the division procedure easier and quicker. If students learn the sectionalisation rules in Maths or the divisibility tests for 1 to xx, they tin can solve the problems in a better mode. For instance, divisibility rules for 13 help us to know which numbers are completely divided by 13. Some numbers similar ii, iii, 4, five have rules which tin exist understood easily. But rules for vii, 11, thirteen, are a little complex and demand to exist understood in-depth.

Mathematics is not easy for some of the states. At times, the demand for tricks and shorthand techniques is felt, to solve Maths problems faster and easily without lengthy calculation. It will also help students to score better marks in exams. These rules are a keen example of such shorthand techniques. In this article, let united states of america discuss the division rules in Maths with many examples.

Table of Contents:

• Definition
• Divisibility of one
• Divisibility of 2
• Divisibility of iii
• Divisibility of 4
• Divisibility of 5
• Divisibility of six
• Divisibility of 7
• Divisibility of 8
• Divisibility of 9
• Divisibility of 10
• Divisibility of 11
• Divisibility of 12
• Divisibility of xiii

Divisibility Test (Division Rules in Maths)

Equally the name suggests, divisibility tests or division rules in Maths aid one to bank check whether a number is divisible by another number without the actual method of partitioning. If a number is completely divisible by another number then the caliber will exist a whole number and the rest will exist zero.

Since every number is not completely divisible by every other number such numbers exit remainder other than zero. These rules are sure ones, which help us to determine the actual divisor of a number simply by considering the digits of the number.

The segmentation rules from i to 13 in Maths are explained hither in detail with many solved examples. Get through the below commodity to learn the shortcut methods to divide the numbers hands.

• Multiplication And Segmentation
• Dividend
• Divisor
• Quotient

Divisibility Rule of ane

Every number is divisible past one. Divisibility rule for 1 doesn't have whatsoever condition. Whatsoever number divided by i will give the number itself, irrespective of how large the number is. For example, 3 is divisible by 1 and 3000 is also divisible by 1 completely.

Divisibility Rule of ii

If a number is fifty-fifty or a number whose last digit is an even number i.eastward.  ii,4,vi,8 including 0, it is always completely divisible by 2.

Case: 508 is an even number and is divisible by 2 merely 509 is not an fifty-fifty number, hence information technology is not divisible by 2. Process to check whether 508 is divisible by 2 or not is every bit follows:

• Consider the number 508
• Just take the last digit 8 and separate information technology by 2
• If the final digit 8 is divisible past 2 and so the number 508 is as well divisible past two.

Divisibility Rules for 3

Divisibility rule for three states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.

Consider a number, 308. To check whether 308 is divisible by 3 or not, take sum of the digits (i.e. 3+0+8= 11). Now cheque whether the sum is divisible past 3 or not. If the sum is a multiple of three, so the original number is also divisible past 3. Here, since 11 is not divisible by 3, 308 is besides not divisible past 3.

Similarly, 516 is divisible past 3 completely equally the sum of its digits i.e. v+1+6=12, is a multiple of 3.

Divisibility Rule of 4

If the concluding 2 digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by four completely.

Example: Take the number 2308. Consider the last two digits i.e.  08. Equally 08 is divisible by four, the original number 2308 is also divisible by 4.

Divisibility Rule of 5

Numbers, which terminal with digits, 0 or v are always divisible past 5.
Example: 10, 10000, 10000005, 595, 396524850, etc.

Divisibility Rule of six

Numbers which are divisible by both ii and three are divisible by 6. That is, if the last digit of the given number is even and the sum of its digits is a multiple of 3, so the given number is also a multiple of 6.

Instance: 630, the number is divisible past two as the last digit is 0.
The sum of digits is half-dozen+three+0 = 9, which is also divisible by 3.
Hence, 630 is divisible by half-dozen.

Divisibility Rules for 7

The rule for divisibility by 7 is a bit complicated which tin be understood by the steps given beneath:

Case: Is 1073 divisible by vii?

• From the dominion stated remove 3 from the number and double information technology, which becomes half-dozen.
• Remaining number becomes 107, so 107-6 = 101.
• Repeating the process 1 more time, nosotros accept 1 10 2 = ii.
• Remaining number 10 – ii = eight.
• As 8 is non divisible past 7, hence the number 1073 is non divisible by 7.

Divisibility Rule of 8

If the terminal three digits of a number are divisible past viii, then the number is completely divisible by viii.

Example: Take number 24344. Consider the last two digits i.eastward.  344. As 344 is divisible by 8, the original number 24344 is likewise divisible by eight.

Divisibility Rule of 9

The rule for divisibility by 9 is similar to divisibility rule for 3. That is, if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Example: Consider 78532, as the sum of its digits (7+8+v+3+2) is 25, which is non divisible past nine, hence 78532 is not divisible past 9.

Divisibility Rule of ten

Divisibility rule for 10 states that any number whose final digit is 0, is divisible by 10.

Example: 10, twenty, thirty, 1000, 5000, 60000, etc.

Divisibility Rules for eleven

If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.

In order to check whether a number similar 2143 is divisible by 11, below is the post-obit procedure.

• Group the alternative digits i.eastward. digits which are in odd places together and digits in fifty-fifty places together. Here 24 and xiii are two groups.
• Take the sum of the digits of each group i.due east. two+4=6 and i+iii= 4
• At present notice the difference of the sums; vi-4=2
• If the divergence is divisible by 11, then the original number is too divisible by 11. Hither ii is the departure which is not divisible by 11.
• Therefore, 2143 is not divisible by 11.

A few more conditions are there to test the divisibility of a number by xi. They are explained here with the help of examples:

If the number of digits of a number is fifty-fifty, then add the first digit and decrease the terminal digit from the rest of the number.

Example: 3784

Number of digits = 4

Now, 78 + 3 – 4 = 77 = 7 × xi

Thus, 3784 is divisible by 11.

If the number of digits of a number is odd, then subtract the get-go and the last digits from the rest of the number.

Example: 82907

Number of digits = five

Now, 290 – eight – seven = 275 × 11

Thus, 82907 is divisible by xi.

Course the groups of 2 digits from the right end digit to the left end of the number and add the resultant groups. If the sum is a multiple of 11, then the number is divisible by 11.

Example: 3774 := 37 + 74 = 111 := 1 + 11 = 12

3774 is not divisible by xi.

253 := 2 + 53 = 55 = 5 × 11

253 is divisible by 11.

Subtract the last digit of the number from the rest of the number. If the resultant value is a multiple of eleven, so the original number will be divisible by eleven.

Example: 9647

9647 := 964 – seven = 957

957 := 95 – 7 = 88 = eight × 11

Thus, 9647 is divisible by eleven.

Divisibility Rule of 12

If the number is divisible past both 3 and 4, and then the number is divisible past 12 exactly.

Example: 5864

Sum of the digits = five + 8 + half dozen + 4 = 23 (not a multiple of 3)

Last 2 digits = 64 (divisible past 4)

The given number 5846 is divisible by 4 merely not past iii; hence, it is not divisible by 12.

Divisibility Rules for thirteen

For any given number, to check if it is divisible by xiii, we take to add four times of the last digit of the number to the remaining number and repeat the procedure until you get a two-digit number.  Now check if that 2-digit number is divisible by thirteen or not. If it is divisible, then the given number is divisible by thirteen.

For example: 2795→ 279 + (5 ten 4)

→ 279 + (20)

→ 299

→ 29 + (nine x 4)

→ 29 + 36

→65

Number 65 is divisible by xiii, xiii x 5 = 65.

Video Lesson

Divisibility Models

Solved Examples

Instance 1:

Check if 288 is divisible by 2.

Solution:

Given, 288 is a number.

If the last digit of 288 is divisible by 2, then 288 is also divisible past ii.

The final digit of 288 is 8, which is divisible by 2, such that;

8/two = 4

Hence, 288 satisfy the divisibility rule for 2.

Example 2:

Check is 195 is divisible by four or non.

Solution:

As nosotros can see, the last digit of 195 is v, which is non divisible past 4.

Hence, 195 is not divisible by 4.

Frequently Asked Questions on Divisibility Rules

What is meant by divisibility rules?

A divisibility test is an easy way to place whether the given number is divided by a fixed divisor without actually performing the division process. If a number is completely divided past another number, then the caliber should be a whole number and the residuum should be zero.

What is the divisibility rule for 2 and 5?

Divisibility rule for 2: The terminal/unit digit of the given number should be an fifty-fifty number or the multiples of ii. (i.e.,) 0, ii, 4, 6, and 8.
Divisibility Rule for five: The unit digit of the given number should be 0 or five.

What is the divisibility rule for 7 and requite an case?

The difference between twice the unit digit of the given number and the remaining part of the given number should exist a multiple of 7 or it should exist zippo. For example, 147 is divisible past vii. Here, the unit digit is 7. When it is multiplied by 2, we go xiv, and the remaining part is xiv. Therefore, the difference between 14 and 14 is 0.

Write down the divisibility rule for nine.

The sum of the digits of the given number should be divisible past 9. For example, 2979 is divisible by 9. (i.e.,) two+9+7+9 = 27, which is divisible by nine.

What is the divisibility dominion for thirteen?

The sum/addition of iv times of the unit of measurement digit and the remaining part of the given number should be a multiple of xiii. For instance, 1092 is divisible past 13. Here, the unit of measurement digit is two. When it is multiplied by 4, nosotros go 8, and the remaining part of the number is 109. Hence, the sum of 109 and eight is 117, which is divisible by xiii.

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How To Check If A Register Is Devisable,

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