If a number is divisible by both 2 and 3, then it is divisible by 6.

We already know that all even numbers are divisible by 2.

So, all even numbers which are divisible by 3 are divisible by 6.

**Example 1 :**

Check whether 5832 is divisible by 6.

**Solution :**

The given number 5832 ends with 2.

So, it is even number and divisible by 2.

Check whether the number 5832 is divisible by 3.

Add all the digits.

5 + 8 + 3 + 2 = 18

The sum of the digits in the given number 5832 is 18 which is a multiple of 3.

Therefore, the given number 5832 is divisible by both 2 and 3.

So, the given number 5832 is divisible by 6.

**Example 2 :**

Check whether 7434 is divisible by 6.

**Solution :**

The given number ends with 4.

So, it is even number and divisible by 2.

Check whether the number 7434 is divisible by 3.

Add all the digits.

7 + 4 + 3 + 4 = 18

The sum of the digits in the given number 7434 is 18 which is a multiple of 3.

Therefore, the given number 7434 is divisible by both 2 and 3.

So, the given number 7434 is divisible by 6.

**Example 3 :**

Check whether 4538 is divisible by 6.

**Solution :**

The given number 4538 ends with 8.

So, it is even number and divisible by 2.

Check whether the number 4538 is divisible by 3.

Add all the digits.

4 + 5 + 3 + 8 = 20

The sum of the digits in the given number 4538 is 20 which is not a multiple of 3.

The given number 4538 is divisible by 2, but not by 3.

So, the given number 4538 is not divisible by 6.

**Example 4 :**

Check whether 1056 is divisible by 6.

**Solution :**

The given number 1056 ends with 6.

So, it is even number and divisible by 2.

Check whether the number 1056 is divisible by 3.

Add all the digits.

1 + 0 + 5 + 6 = 7

The sum of the digits in the given number 1056 is 7 which is a multiple of 3.

Therefore, the given number 1056 is divisible by 2, but not by 3.

So, the given number 1056 is not divisible by 6.

**Example 5 :**

Check whether 2105 is divisible by 6.

**Solution :**

The given number 2105 ends with 5.

So, it is not an even number and it is not divisible by 2.

Therefore, the given number 2105 is not divisible by 6.

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

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**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**

**Trigonometry 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**