# Divisibility Rule by 6

If the given number is divisible by 2 and 3 both
then we can say that the number is divisible by 6.

**Example : **Is **54** divisible by 6?

**Solution : **First check whether the given number is divisible
by 2 or not. Then only check for 3.

Number is **divisible by 2 if its last digits are
0, 2, 4, 6 or 8.**

Here **last digit of a number 54 is 4** means divisible by 2.

Now check for 3 whether the given number is
divisible by 3 or not.

Number is **divisible by 3 if sum of all digits are
multiple of 3 or divisible by 3.**

Here sum of all digits of given number is **54
i.e. 5 + 4 = 9 **Which is multiple of 3. Means 54 is divisible by 3 also.

Hence **54** is divisible by 6.

**Example : **Is **682** divisible by 6?

**Solution : **First check whether the given number is divisible
by 2 or not. Then only check for 3.

Number is **divisible by to if its last digits are
0, 2, 4, 6 or 8.**

Here **last digit of a number 682 is 2** means divisible by 2.

Now check for three whether the given number is
divisible by 3 or not.

Number is **divisible by 3 if sum of all digits are
multiple of 3 or divisible by 3.**

Here sum of all digits of given number is **682
i.e. 6 + 8 + 2 = 16 **Which is not multiple of 3 or we can say **16 is not
divisible by 3.** Means **682** is not divisible by 3.

**Hence 682 is not divisible by 6. **

**Example : **Is **84561** divisible by 6?

**Solution : **First check whether the given number is divisible
by 2 or not. Then only check for 3.

Number is divisible by to if its last digits are
0, 2, 4, 6 or 8.

Here **last digit of a number 84561 is 1
means not divisible by 2.**

**There is no need to check further that 84561 is
divisible by 3 or not. Because number is only divisible by 6 if its divisible
by 2 and 3 both.**

Here in this case number is not divisible by 2.
Hence **84561 **is not divisible by 6.

Let's have practice for divisibility rule by 6.

**297, 286, 2664, 6588, 8451, 86586, 95642**

**Solution : **

**297** - **Last digit 7** means **not divisible by 2**.
Hence **not divisible by 6**.

**286** - **Last digit is 6** which is **divisible by 2**. **(2
+ 8 + 6 = 16) **16 is **not divisible by 3.**

**Hence not divisible by 6. **

**2664** - **Last digit is 4** which is **divisible by 2**.
**(2 + 6 + 6 + 4 = 18 )** 18 is **divisible by 3.**

**Hence divisible by 6. **

**6588** - **Last digit is 8 **which is **divisible by 2**. **(
6 + 5 + 8 + 8 = 27)** 27 is **divisible by 3.**

**Hence divisible by 6. **

**8451** - **Last digit 1** means **not divisible by 2**.
Hence **not divisible by 6.**

**86586** - **Last digit is 6** which is **divisible by 2**.
**( 8 + 6 + 5 + 8 + 6 = 33)** 33 **is divisible by**

**3. Hence divisible by 6.**

**95642** - **Last digit is 2** which is **divisible by 2**. **( 9 + 5 + 6 + 4 + 2 =26)** 26 **is not divisible ****by 3. Hence not divisible by 6.**

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