# Divisible by 11

Divisible by 11 is discussed below.

A number is divisible by 11 if the sum of the digits in the odd places and the sum of the digits in the even places difference is a multiple of 11 or zero.

Consider the following numbers which are divisible by 11, using the test of divisibility by 11:

(i) 154, (ii) 814, (iii) 957, (iv) 1023, (v) 1122, (vi) 1749, (vii) 53856, (viii) 592845, (ix) 5048593, (x) 98521258.

(i) 154

Sum of the digits in the even place (Red Color)  = 5

Sum of the digits in the odd places (Black Color) = 1 + 5 = 6

Difference between the two sums = 5 - 6 = – 1

-1 is divisible by 11.

Hence, 154 is divisible by 11.

(ii) 814

Sum of the digits in the even place (Red Color)  = 1

Sum of the digits in the odd places (Black Color) = 8 + 4 = 12

Difference between the two sums = 1 - 12 = – 11

-11 is divisible by 11.

Hence, 814 is divisible by 11.

(iii) 957

Sum of the digits in the even place (Red Color)  = 5

Sum of the digits in the odd places (Black Color) = 9 + 7 = 16

Difference between the two sums = 5 - 16 = – 11

-11 is divisible by 11.

Hence, 957 is divisible by 11.

(iv) 1023

Sum of the digits in the even places (Red Color)  = 0 + 3 = 3

Sum of the digits in the odd places (Black Color) = 1 + 2 = 3

Difference between the two sums = 3 - 3 = 0

0 is divisible by 11.

Hence, 1023 is divisible by 11.

(v) 1122

Sum of the digits in the even places (Red Color)  = 1 + 2 = 3

Sum of the digits in the odd places (Black Color) = 1 + 2 = 3

Difference between the two sums = 3 - 3 = 0

0 is divisible by 11.

Hence, 1122 is divisible by 11.

(vi) 1749

Sum of the digits in the even places (Red Color)  = 7 + 9 = 16

Sum of the digits in the odd places (Black Color) = 1 + 4 = 5

Difference between the two sums = 16 - 5 = 11

11 is divisible by 11.

Hence, 1749 is divisible by 11.

(vii) 53856

Sum of the digits in the even places (Red Color)  = 3 + 5 = 8

Sum of the digits in the odd places (Black Color) = 5 + 8 + 6 = 19

Difference between the two sums = 8 - 19 = -11

-11 is divisible by 11.

Hence, 53856 is divisible by 11.

(viii) 592845

Sum of the digits in the even places (Red Color) = 9 + 8 + 5 = 22

Sum of the digits in the odd places (Black Color) = 5 + 2 + 4 = 11

Difference between the two sums = 22 - 11 = 11

11 is divisible by 11.

Hence, 592845 is divisible by 11.

(ix) 5048593

Sum of the digits in the even places (Red Color) = 0 + 8 + 9 = 17

Sum of the digits in the odd places (Black Color) = 5 + 4 + 5 + 3 = 17

Difference between the two sums = 17 - 17 = 0

0 is divisible by 11.

Hence, 5048593 is divisible by 11.

(x) 98521258

Sum of the digits in the even places (Red Color) = 8 + 2 + 2 + 8 = 20

Sum of the digits in the odd places (Black Color) = 9 + 5 + 1 + 5 = 20

Difference between the two sums = 20 - 20 = 0

0 is divisible by 11.

Hence, 98521258 is divisible by 11.

Multiplication Magic of 11:

Multiplication of 11 by 13 i.e., 13 × 11

Add the digits of that number which is multiplied by 11 i.e., in 13, 1 + 3 = 4.

Introduce this number in the middle of 13.

Now, the product of 13 × 11 will be 143, i.e., 13 × 11 = 143

To check whether a number is divisible by 11, we find the sum of the digits in the even places and the odd places separately. Now, check the difference between the two sums if it is 0 or divisible by 11, then the given number is divisible by 11.

For example:

1. Is 852346 divisible by 11?

Solution:

Sum of digits in even places (Red Color) = 5 + 3 + 6 = 14

Sum of digits in odd places (Black Color) = 8 + 2 + 4 = 14

Difference = 14 - 14 = 0

Therefore, 852346 is divisible by 11.

2. Is 85932 divisible by 11?

Solution:

Sum of digits in even places (Red Color) = 5 + 3 = 8

Sum of digits in odd places (Black Color) = 8 + 9 + 2 = 19

Difference = 8 - 19 = -11

-11 is divisible by 11.

Therefore, 85932 is divisible by 11.

3. Check whether 27896 is divisible by 11 or not.

Solution:

The sum of the digits at add places is (2 + 8 + 6) = 16.

The sum of the digits at even places is (7 + 9) = 16.

Their difference is 16 - 16 = 0, which is divisible by 11.

Therefore, the number 27896 is divisible by 11.

4. Check the divisibility of the given numbers by 11.

(i) 45982

(ii) 694201

(iii) 102742

(iv) 73953

(v) 326117

(vi) 5676

Answer: (i) 45982 is not divisible by 11.

(ii) 694201 is not divisible by 11.

(iii) 102742 is not divisible by 11.

(iv) 73953 is divisible by 11.

(v) 326117 is divisible by 11.

(vi) 5676 is divisible by 11.

## You might like these

• ### Even and Odd Numbers Between 1 and 100 | Even and Odd Numbers|Examples

All the even and odd numbers between 1 and 100 are discussed here. What are the even numbers from 1 to 100? The even numbers from 1 to 100 are:

• ### 5th Grade Factors and Multiples Worksheets | L.C.M. | H.C.F. | Answers

In 5th Grade Factors and Multiples Worksheets we will find the multiples of a given number, find the prime factors of a number, HCF of co-prime number, LCM of two co-prime numbers, HCF of two co-prime numbers, common multiples of three numbers, word problems on LCM and word

• ### Worksheet on Divisibility Rules | Questions on Test of Divisibility

Worksheet on divisibility rules will help us to practice different types of questions on test of divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. We need to use the divisibility rules to find whether the given number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

• ### Word Problems on H.C.F. and L.C.M. | Least Common Multiple | GCF Math

Here we will get the idea how to solve the word problems on H.C.F and L.C.M. 1. Find the smallest number which on adding 19 to it is exactly divisible by 28, 36 and 45. First we find the least

• ### Worksheet on Word Problems on H.C.F. and L.C.M. |Highest Common Factor

In worksheet on word problems on H.C.F. and L.C.M. we will find the greatest common factor of two or more numbers and the least common multiple of two or more numbers and their word problems. I. Find the highest common factor and least common multiple of the following pairs

• ### Relationship between H.C.F. and L.C.M. |Highest Common Factor|Examples

The product of highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of two numbers is equal to the product of two numbers i.e., H.C.F. × L.C.M. = First number × Second number or, LCM × HCF = Product of two given numbers

• ### Worksheet on L.C.M. | Least Common Multiple Worksheets |LCM Worksheets

Practice the questions given in the worksheet on l.c.m. to find the least common multiple by listing their multiples, by common prime factors and by division method. I. Find the L.C.M. of the following by listing their multiples. (i) 5, 10, 15 (ii) 4, 10, 12 (iii) 3, 9, 12

• ### Least Common Multiple |Lowest Common Multiple|Smallest Common Multiple

The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number. The lowest common multiple or LCM of two or more numbers is the smallest of all common multiples.

• ### Multiples | Multiples of a Number |Common Multiple|First Ten Multiples

What are multiples? ‘The product obtained on multiplying two or more whole numbers is called a multiple of that number or the numbers being multiplied.’ We know that when two numbers are multiplied the result is called the product or the multiple of given numbers.

• ### Worksheet on H.C.F. | Word Problems on H.C.F. | H.C.F. Worksheet | Ans

Practice the questions given in the worksheet on hcf (highest common factor) by factorization method, prime factorization method and division method. Find the common factors of the following numbers. (i) 6 and 8 (ii) 9 and 15 (iii) 16 and 18 (iv) 16 and 28

• ### Highest Common Factor |Find the Highest Common Factor (H.C.F)|Examples

Highest common factor (H.C.F) of two or more numbers is the greatest number which divides each of them exactly. Now we will learn about the method of finding highest common factor (H.C.F). Steps 1: Find all the factors of each given number. Step 2: Find common factors of the

• ### Worksheet on Methods of Prime Factorization |Prime Factors by Division

Practice the questions given in the worksheet on methods of prime factorization. 1. Each of the following is the prime factorization of a certain number. Find the number. (i) 2 × 5 × 7

• ### Prime Factorisation |Complete Factorisation |Tree Factorisation Method

Prime factorisation or complete factorisation of the given number is to express a given number as a product of prime factor. When a number is expressed as the product of its prime factors, it is called prime factorization. For example, 6 = 2 × 3. So 2 and 3 are prime factors

• ### Divisible by 9 | Test of Divisibility by 9 |Rules of Divisibility by 9

A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9. Consider the following numbers which are divisible by 9, using the test of divisibility by 9:

• ### Divisible by 10|Test of Divisibility by 10|Rules of Divisibility by 10

Divisible by 10 is discussed below. A number is divisible by 10 if it has zero (0) in its units place. Consider the following numbers which are divisible by 10, using the test of divisibility by 10:

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Adding 1-Digit Number | Understand the Concept one Digit Number

Sep 18, 24 03:29 PM

Understand the concept of adding 1-digit number with the help of objects as well as numbers.

2. ### Addition of Numbers using Number Line | Addition Rules on Number Line

Sep 18, 24 02:47 PM

Addition of numbers using number line will help us to learn how a number line can be used for addition. Addition of numbers can be well understood with the help of the number line.

3. ### Counting Before, After and Between Numbers up to 10 | Number Counting

Sep 17, 24 01:47 AM

Counting before, after and between numbers up to 10 improves the child’s counting skills.

4. ### Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 17, 24 12:10 AM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…