Divisibility Rules : Complete Guide with Examples

Mathematics is full of patterns, and divisibility rules are one of the most charming tools we use to discover those patterns. These policies permit us to decide whether one variety is divisible by every other, without having to do a long division. Understanding what is divisibility regulations and how they work could make calculations quicker and less difficult.

Table of Contents

• What Are Divisibility Rules?
• What Is Divisibility?
• Divisibility Rules Chart (1 to 20)
• Basic Divisibility Rules (1 to 10)
• Advanced Divisibility Rules (11 to 20)
• Divisibility Rules Examples
• Misconceptions About Divisibility Rules
• Fun Facts
• Solved Examples
• Conclusion
• Frequently Asked Questions on Divisibility Rules

 

What Are Divisibility Rules?

Divisibility guidelines are shortcut techniques used in mathematics to decide whether one quantity can be divided by another without performing full division. These rules help you quickly check if a number is divisible by using some other the usage of simple methods like analysing the digits or their sum. For instance, if the sum of a variety of digits is divisible by 3, then the entire number is divisible with the aid of 3. These rules are especially beneficial in checks, aggressive checks, intellectual math, and real-world conditions in which brief calculations are required. Understanding what's divisibility regulations can significantly improve your quantity feel and velocity in solving troubles.

 

What Is Divisibility?

Divisibility refers to the properties where one wide variety may be divided by another without leaving a remainder. For example, in case you divide 20 with the aid of five and get a whole wide variety (four), then 20 is divisible by 5. When we ask what's divisibility, we're essentially checking if a number can be cut up into smaller, equal elements with the use of some other wide variety. These regulations make it less difficult to simplify numbers, component them effectively, and resolve complex issues, frequently while not having a calculator or prolonged division.

Divisibility Rules Chart (1 to 20)

 

 

Basic Divisibility Rules (1 to 10)

Divisibility by  1

Every variety is divisible by 1

There’s no unique rule required.

 

Divisibility by 2

If the remaining digit is even (0, 2, 4, 6, 8), the wide variety is divisible by 2.

 

Divisibility by 3

Add all the digits.

If the result is divisible by using 3, so is the unique range.

 

Divisibility by 4

Look at the final digits.

If they form various numbers divisible by four, then the whole number is just too.

 

Divisibility by 5

Ends in both 0 and 5.

 

Divisibility by 6

Satisfies each divisibility by 2 and 3.

 

Divisibility by  7

Double the final digit and subtract it from the rest.

If the result is divisible by way of 7, so is the variety.

 

Divisibility by 8

Check the ultimate three digits.

If they shape a number divisible using 8, then so is the whole wide variety.

 

Divisibility by 9

Add all the digits.

If the sum is divisible by 9, then the quantity is as well.

 

Divisibility by 10

Must end in 0.

 

Advanced Divisibility Rules (11to 20)

Divisibility by 11

Take the alternating sum of digits.

If this sum is divisible by eleven, then so is the number.

 

Divisibility by 12

If the number is divisible by means of each 3 and 4, then it's miles divisible by using 12.

 

Divisibility by 13

Add 4 instances of the closing digit to the closing digits.

Repeat until a viable wide variety is done.

 

Divisibility by14

Must fulfill divisibility rules of 2 and 7.

 

Divisibility by15

Must fulfill divisibility by using 3 and 5.

 

Divisibility by16

The last four digits must be divisible by way of 16.

Divisibility using the subtraction of 5 instances of the last digit from the closing number.

 

Divisibility by 18

Must be divisible via 2 and 9.

 

Divisibility by 19

Add two times the last digit to the rest and repeat the method.

 

Divisibility by 20

Ends with 0, and the quantity before the last must be even.

 

Divisibility Rules Examples

Example 1: Is 462 divisible by way of 3?

Sum = 4+6+2 = 12  divisible by using 3 Yes.

 

Example 2: Is 1,248 divisible by way of four?

The last two digits =48, divisible by 4. Yes.

 

Example 3: Is 3355 divisible last means of 5?

Ends in 5  Yes.

 

Example 4: Is 1441 divisible through 11?

Alternating sum = 1−4+4−1 = 0. Yes.

 

Example 5: Is 1020 divisible by 20?

Ends in 0, the second-final digit is even (2)  Yes

 

Misconceptions About Divisibility Rules

All even numbers are divisible through four

False: Only if the closing digits are divisible by four.

 

If a number is divisible by 3, it is divisible by 6

False: It should additionally be even.

 

All numbers ending in 5 are divisible by way of 10

False: Must end in 0 to be divisible via 10.

 

Rules may be used for decimals.

False: Divisibility guidelines work most effectively on complete numbers, no longer decimals.

 

Divisibility via 7 and effectively critical

False: Very useful in exams and puzzles.

 

Fun Facts

Barcodes & ISBN Numbers

Use divisibility policies for errors-checking the usage of mod 10 or 11.

 

Digital Puzzles & Aptitude Tests

Many puzzles in competitive assessments check divisibility logic.

 

Banking & Finance

Used in validating massive batches of numbers like account digits.

 

Programming & Algorithms

Divisibility assessments assist in writing optimized codes.

 

Cryptography

Modular arithmetic is predicated closely on these policies for encoding.

 

Solved Examples

Example 1: Is 231 divisible by using 3?

  2+3+1 = 6  divisible by 3 Yes

 

Example 2: Is 1274 divisible by using 2 and 7?

  The last digit, four  divisible by 2

  Apply 7-rule: 127 − 2×4 = 127−8= 119  divisible with the aid of 7  Yes

 

Example 3: Is 4620 divisible by way of 5 and 3?

Ends in 0  divisible with the aid of 5

Sum = 4+6+2+0 = 12  divisible using 3. Yes

 

Example 4: Is 7896 divisible by using four?

Last  digits = 96  96 ÷ 4 = 24  Yes

 

Example 5: Is 123456789 divisible by way of 9?

Sum = 45  divisible by 9  Yes

 

Conclusion

Learning divisibility policies is like unlocking a fixed of secret shortcuts in math. Whether you're simplifying numbers, making ready for exams, or fixing common sense puzzles, those gear are invaluable. By knowing what responsibility policies are, training diversity guidelines, and knowing and warding off commonplace errors, you may greatly enhance your diversity feel. So, preserve this manual available, mastering divisibility is one step toward learning arithmetic!

 

Related Link

Divisibility: Explore divisibility rules with Orchids The International School and boost your math skills effortlessly.

Divisibility Rule of 7:  Learn the smart trick for divisibility by 7 at Orchids The International School and solve faster.

 

Frequently Asked Questions on Divisibility Rules

1. What are the divisibility rules of 2 to 11?

• 2= A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8).

• 3= Add the digits. If the sum is divisible by 3, so is the number.

• 4= Check the last two digits. If they form a number divisible by 4, the entire number is.

• 5= If the number ends in 0 or 5, it's divisible by 5.

• 6=If a number is divisible by both 2 and 3, it’s divisible by 6.

• 7=Double the last digit and subtract it from the rest. If the result is divisible by 7, so is the number.

• 8=If the last three digits form a number divisible by 8, so is the whole number.

• 9=If the sum of the digits is divisible by 9, the number is divisible by 9.

• 10=If the number ends in 0, it is divisible by 10

• 11=Subtract and add digits alternately. If the alternating sum is divisible by 11 (or equals 0), the number is divisible by 11.

 

2. What is the divisibility rule of 11111?

There is no standard divisibility rule for 11111 like there is for small numbers. To check if a number is divisible by 11111, divide it directly or use factoring (if possible). 11111 is a prime number, so it's only divisible by 1 and itself unless part of a specific pattern.

 

3. What is divisible by 101?

Any number that is a multiple of 101 (e.g., 101, 202, 303, 404...) is divisible by 101.
To test if a large number is divisible by 101, you generally divide it directly since there is no common divisibility shortcut for 101.

 

4. How to d divisible by 1?

Every integer is divisible by 1.
No test or calculation is needed, any whole number divided by 1 equals itself, with no remainder.

 

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