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.

$Divisible by 11$

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.

● 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

4th Grade Factors and Multiples Worksheet | Factors & Multiples

In 4th grade factors and multiples worksheet we will find the factors of a number by using multiplication method, find the even and odd numbers, find the prime numbers and composite numbers, find the prime factors, find the common factors, find the HCF(highest common factors
Examples on Multiples | Different Types of Questions on Multiples

Examples on multiples on different types of questions on multiples are discussed here step-by-step. Every number is a multiple of itself. Every number is a multiple of 1. Every multiple of a number is either greater than or equal to the number. Product of two or more numbers
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
Word Problems on L.C.M. | L.C.M. Word Problems | Questions on LCM

Let us consider some of the word problems on l.c.m. (least common multiple). 1. Find the lowest number which is exactly divisible by 18 and 24. We find the L.C.M. of 18 and 24 to get the required number.
Word Problems on H.C.F | H.C.F. Word Problems | Highest Common Factor

Let us consider some of the word problems on H.C.F. (highest common factor). 1. Two wires are 12 m and 16 m long. The wires are to be cut into pieces of equal length. Find the maximum length of each piece. 2.Find the greatest number which is less by 2 to divide 24, 28 and 64
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.
Common Multiples | How to Find Common Multiples of Two Numbers?

Common multiples of two or more given numbers are the numbers which can exactly be divided by each of the given numbers. Consider the following. (i) Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, …………etc. Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, …………… etc.
Worksheet on Multiples | Questions on Multiples | Exercise Sheet

In worksheet on multiples of that numbers, all grade students can practice the questions on multiples. This exercise sheet on multiples can be practiced by the students to get more ideas on the numbers that are being multiplied. 1. Write any four multiples of: 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
Prime Factors | Prime Factors of a Number | First Prime Number | Prime

Prime factor is the factor of the given number which is a prime number also. How to find the prime factors of a number? Let us take an example to find prime factors of 210. We need to divide 210 by the first prime number 2 we get 105. Now we need to divide 105 by the prime
Properties of Multiples | With Examples | Multiple of each Factor

The properties of multiples are discussed step by step according to its property. Every number is a multiple of 1. Every number is the multiple of itself. Zero (0) is a multiple of every number. Every multiple except zero is either equal to or greater than any of its factors
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
To find Highest Common Factor by using Division Method | Method

In this method we first divide the greater number by the smaller number. The remainder becomes the new divisor and the previous divisor as the new dividend. We continue the process until we get 0 remainder. Finding highest common factor (H.C.F) by prime factorization for
Method of H.C.F. |Highest Common Factor|Factorization &Division Method

We will discuss here about the method of h.c.f. (highest common factor). The highest common factor or HCF of two or more numbers is the greatest number which divides exactly the given numbers. Let us consider two numbers 16 and 24.

● Divisibility Rules.

5th Grade Math Problems

From Divisible by 11 to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

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.

[?]Subscribe To This Site

$XML RSS$

E-mail Address

First Name

Then Don't worry — your e-mail address is totally secure. I promise to use it only to send you Math Only Math.