**Divisibility by 11 :**

If the difference between the sum of one set of alternate digits and the sum of the other set of alternate digits is 0 or 11 or 22.....the numbers are divisible by 11.

By considering the numbers 121, 132, 143, 154, 165, 176, 187, 198 all these numbers are divisible by 11.

In 121 , 1 + 1 = 2[Which is equal to the middle number]

In 143 , 1 + 3 = 4[Which is equal to the middle number]

In 165 , 1 + 5 = 6[Which is equal to the middle number]

**Example 1 :**

Test whether 198 is divisible by 11?

**Solution :**

In this three digit number the sum of the first and last number = middle number that is ** 1 + 8 = 9 **
So the whole number 198 is divisible by 11.

**Example 2 :**

Test whether 473 is divisible by 11 ?

**Solution :**

In the given number 473, the sum of the first and last number = middle number that is **4 + 3 = 7.**

Hence, the whole number 473 is divisible by 11.

By considering the following 4 digit numbers 2563, 3498, 5137, 6369.

The above four digit numbers are divisible by 11.

In 2563 , 2 + 6 = 8 , 5 + 3 = 8 , 8 - 8 = 0

In 3498 , 3 + 9 = 12 , 4 + 8 = 12 , 12 - 12 = 0

In 5137 , 5 + 3 = 8 , 1 + 7 = 8 , 8 - 8 = 0

**Example 3 :**

Test whether 6369 is divisible by 11 ?

**Solution :**

In the given four digit number 6369, the sum of the first and last number = middle number that is **6 + 6 = 12, 3 + 9 =12 , 12 - 12 = 0 **

Hence, the given number 6369 is divisible by 11.

After having gone through the stuff given above, we hope that the students would have understood "Divisibility by 11"

Apart from the stuff given above, if you want to know more about "Divisibility by 11", please click here.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Math dictionary**