Topic Included: | Formulas, Definitions & Exmaples. |

Main Topic: | Quantitative Aptitude. |

Quantitative Aptitude Sub-topic: | Number System Aptitude Notes & Questions. |

Questions for practice: | 10 Questions & Answers with Solutions. |

The divisibility rule is the way to identify whether a number is divisible by any other number completely or not, without performing the actual division process. A number is completely divisible by another number if there is no remainder after division.

A number is divisible by 2, if the unit digit of the number is zero or divisible by 2, then the number is also divisible by 2. All even numbers are divisible by 2.

**Example:** Numbers 2, 4, 6, 8, 10, 12, 18, 64, 444, 5420, 8322, etc. are divisible by 2 because all are even numbers, and also the unit digit of numbers is either zero or divisible by 2. Hence all the numbers are divisible by 2.

A number is divisible by 3, if the sum of all the digits of the number is divisible by 3, then the number is also divisible by 3.

**Example:** A number 4311 is divisible by 3 because the sum of its digits (4 + 3 + 1 + 1) is 9, and 9 is divisible by 3, Hence the number 4311 is also divisible by 3.

A number is divisible by 4, if the last two-digit of the number is divisible by 4, then the number is also divisible by 4.

**Example:** The number 4344 is divisible by 4 because the last two-digit of the number (44) is divisible by 4, Hence the number 4344 is also divisible by 4.

A number is divisible by 5 if the unit digit of the number is zero or 5, then the number is divisible by 5.

**Example:** Numbers 40, 545, 7560, 8565, etc. are divisible by 5 because the unit digit of numbers is either zero or 5. Hence these numbers are divisible by 5.

A number is divisible by 6 if the last digit of the number is divisible by 2, and also the sum of all the digits is divisible by 3, then the number is divisible by 6.

**Example:** A number 7536 is divisible by 6 because the last digit of the number (6) is divisible by 2, and also the sum of all the digits (7 + 5 + 3 + 6) of the number is 21, which is divisible by 3. Hence the number 7536 is divisible by 6.

A number is divisible by 7 if the unit digit of the number is multiplied by 2 and subtracted by the remaining number, and if the result is divisible by 7, then the original number is also divisible by 7.

A - 2B = C

Where B is the unit digit

A is the remaining number other than unit digit.

C is the result.

Here, if C is divisible by 7, then the original number is also divisible by 7.

**Example:** Let's take a number 1554

Here B = 4

A = 155, then

A - 2B = C

155 - 8 = C

C = 147

Here the number 147 is divisible by 7, Hence the number 1554 is also divisible by 7.

A number is divisible by 8 if the last three-digit of the number is divisible by 8, then the number is also divisible by 8.

**Example:** A number 45672 is divisible by 8 because the last three-digit 672 is divisible by 8. Hence the number 45672 is also divisible by 8.

A number is divisible by 9 if the sum of all the digits of the number is divisible by 9, then the number is also divisible by 9.

**Example:** A number 2349 is divisible by 9 because the sum of the number (2 + 3 + 4 + 9) is 18, which is divisible by 9. Hence the number 2349 is also divisible by 9.

A number is divisible by 10 if the unit digit of the number is zero, then the number is divisible by 10.

**Example:** The numbers 100, 250, 530, 840, 1060, etc. are divisible by 10 because the unit digit of these numbers is zero. Hence all the numbers are divisible by 10.

A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places of any number is either zero or divisible by 11, then the number is divisible by 11.

**Example:** A number 601590 is divisible by 11 because the difference between the sum of digits at odd places (1 + 9 + 6 = 16) and the sum of digits at even places (0 + 5 + 0 = 5) is (16 - 5 = 11), which is divisible by 11, Hence the number 601590 is also divisible by 11.

A number is divisible by 12 if the number is divisible by 3 and 4 both, then the number also divisible by 12.

**Example:** The numbers 132, 180, 192, etc. are divisible by 12 because all the numbers are divisible by 3 and 4 both. Hence all the numbers are also divisible by 12.

A number is divisible by 13 if the unit digit of the number is multiplied by 4 and added with the remaining number, then if the result is divisible by 13, the original number is also divisible by 13.

A + 4B = C

Where B is the unit number.

A is the remaining number other than unit digit.

and C is the result.

Here, if result C is divisible by 13, then the original number is also divisible by 13.

**Example:** Let's take a number 702

Here B = 2

A = 70, then

A + 4B = C

70 + 8 = C

C = 78

Here the number 78 is divisible by 13, Hence the number 702 is also divisible by 13.

A number is divisible by 14 if the number is divisible by 2 and 7 both, then the number also divisible by 14.

**Example:** The numbers 168, 196, etc. are divisible by 14 because all the numbers are divisible by 2 and 7 both. Hence all the numbers are also divisible by 14.

A number is divisible by 15 if the unit digit of any number is zero or 5, as well as the sum of all the digits divisible by 3, then the number is divisible by 15.

**Example:** The numbers 480, 555, etc. are divisible by 15 because the unit digit of all the numbers is zero or 5, as well as the sum of all the digits, is divisible by 3. Hence the numbers 480 and 555 are divisible by 15.

A number is divisible by 16 if the last four-digit of any number is divisible by 16 then that number is also divisible by 16.

**Example:** A number 5401920 is divisible by 16 because the last four-digit of the number 1920, is divisible by 16. Hence the number 5401920 is also divisible by 16.

A number is divisible by 17 if the unit digit of any number is multiplied by 5 and subtracted by the remaining number, then if the result is divisible by 17, the original number is also divisible by 17.

A - 5B = C

Where B is the unit digit

A is the remaining number other than the unit digit.

and C is the result.

Here, if the result C is divisible by 17, then the original number is also divisible by 17.

**Example:** Let's take a number 816

Here B = 6

A = 81, then

A - 5B = C

81 - 30 = C

C = 51

Here the number 51 is divisible by 17, Hence the number 816 is also divisible by 17.

A number is divisible by 18 if the number is divisible by 2 and 9 both, then the number is also divisible by 18.

**Example:** The numbers 216, 270, 324, etc. are divisible by 18 because all the numbers are divisible by 2 and 9 both. Hence all the numbers are also divisible by 18.

A number is divisible by 19 if the unit digit of the number is multiplied by 2 and added with the remaining number, and then if the result is divisible by 19, the original number is also divisible by 19.

A + 2B = C

Where B is the unit digit.

A is the remaining number other than the unit digit.

and C is the result.

Here, if result C is divisible by 19, then the original number is also divisible by 19.

**Example:** Let's take a number 2508

Here B = 8

A = 250, then

A + 2B = C

250 + 16 = C

C = 266

Here the number 266 is divisible by 19, Hence the number 2508 is also divisible by 19.

A number is divisible by 20 if any number is divisible by 4 and 5 both, then the number also divisible by 20.

**Example:** A number 2,000 is divisible by 20 because the number is divisible by 4 and 5 both. Hence the number is also divisible by 20.

Lec 1: Introduction to Number System
Lec 2: Factors of Composite Number
Questions and Answers-1
Lec 3: Basic Remainder Theorem
Questions and Answers-2
Lec 4: Polynomial Remainder Theorem
Questions and Answers-3
Questions and Answers-4
Questions and Answers-5
Lec 5: LCM of Numbers
Questions and Answers-6
Lec 6: HCF of Numbers
Questions and Answers-7
Questions and Answers-8
Lec 7: Divisibility Rules of Numbers
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Questions and Answers-10
Questions and Answers-11
Questions and Answers-12
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