Divisibility Rule of 6
The divisibility rule of 6 states that a number is divisible by 6 if it is divisible by the number 2 and 3 both. For this, we need to check the divisibility test of 2 and the divisibility test of 3. Divisibility rules help in solving problems easily without using the division concept.
What is the Divisibility Rule of 6?
A whole number is said to be divisible by 6 if it fulfills the two conditions given below.
 The whole number has to be divisible by 2. A number is divisible by 2 if the unit place digit of the number is even, i.e 0, 2, 4, 6, and 8.
 The whole number has to be divisible by 3. A number is divisible by 3 if the sum of all digits of the number is a multiple of 3 or the sum is exactly divisible by 3.
Both the conditions should apply to the number while doing the divisibility test of 6. If a number does not fulfill any one of the given conditions or both then we can say that a number is not divisible by 6. In other words, we can say that all the even numbers that come in the multiplication table of 3 are divisible by 6.
Let's understand the divisibility rule of 6 with the help of examples.
a) Applying divisibility test of 6 on the number 9156
Condition one: Number has to be divisible by 2 ⇒ 9156 ends with an even number (6). It is divisible by 2 [9156 ÷ 2 = 4578].
Condition two: Number has to be divisible by 3. The sum of the digits of the number 9156 is 21 (9 + 1 + 5 + 6 = 21). The sum 21 is divisible by 3. The number 9156 is divisible by 3.
Thus, 9156 is divisible by both 2 and 3. Therefore, it is divisible by 6.
b) Applying divisibility rule of 6 on the number 825.
Condition one: Number has to be divisible by 2 ⇒ 825 ends with an odd number (5). It is NOT divisible by 2.
Condition two: Number has to be divisible by 3. The sum of the digits of the number 825 is 15 (8+ 2 + 5 = 15). The sum 15 is divisible by 3. The number 825 is divisible by 3 (825 ÷ 3 = 275).
We can see that 825 is NOT divisible by 2 and it is divisible by 3. Since the number is not meeting one condition, therefore, 825 is NOT divisible by 6.
Divisibility Rule of 6 for Large Numbers
The divisibility rule of 6 is the same for all numbers whether it is a smaller number or a large number. A large number is divisible by 6 if it is divisible by the numbers 2 and 3 both. The large number should satisfy both the conditions of the divisibility test of 6.
Follow the steps to check if a large number is divisible by 6 or not.
 Step 1: Check the unit place digit of the number. If it is even, it is divisible by 2 and if it is odd, it is NOT divisible by 2.
 Step 2: Check the sum of all digits of the number. If the sum is divisible by 3 then the number is also divisible by 3.
 Step 3: If step 1 and step 2 say that the large number is divisible by 2 and 3 both then the large number is said to be divisible by 6.
For example, 145962
 Step 1: The number is even, so it is divisible by 2.
 Step 2: The sum of all digits is 1+4+5+9+6+2 = 27, yes the sum 27 is divisible by 3 which means 145962 is also divisible by 3. Note that the sum of the digits of the number 27 is 2 + 7 = 9 is also divisible by 3. We can repeat this process to get the sum closer to 3.
 Step 3: The number 145962 is divisible by 2 and 3 both. Therefore, the number 145962 is divisible by 6.
Divisibility Rule of 6 and 7
The divisibility rules of 6 and 7 are completely different. The divisibility rule of 6 states that the number should divisible by 2 and 3 both, if the number is divisible by 2 and 3 both, the number said to be divisible by 6, whereas the divisibility rule for 7 states that for a number to be divisible by 7, multiply the ones place digit of the number by 2, and subtract it with the rest of the number to its left leaving the digit at the unit place. If the result is either 0 or a multiple of 7, then the number is divisible by 7.
Divisibility Test of 6 and 9
Both the divisibility rules of 6 and 9 are different from each other. In the divisibility rule of 6, we check whether the number is divisible by 2 and 3 or not, while in the divisibility test of 9, we calculate the sum of all the digits of the number. If the sum of the digits is a number divisible by 9, then the given number is also divisible by 9. Let us take an example to understand it better. To find out whether 450 is divisible by 6 and 9, we first check its divisibility by 2 and 3. The unit place digit of 450 is 0, so it is divisible by 2, and the sum of the digits is 4+5+0= 9, which is divisible by 3. So, 450 is divisible by 6. Now, as we have already calculated that the sum of the digits of 450 is 9, which is divisible by 9. Hence, 450 is divisible by both 6 and 9.
Related Articles to Divisibility Rule of 6
Check the following pages similar to the divisibility rule of 6.
Divisibility Rule of 6 Examples

Example 1: Find out whether the given numbers are divisible by 6 or not, using the test of divisibility by 6.
a)80
b)264Solution: a) As 80 is an even number it is divisible by 2, but the sum of the digits that is, 8 + 0 = 8 is not divisible by 3, so 80 is not divisible by 3. Thus the number 80 is not divisible by 6 because it is divisible by 2 but not divisible by 3.
b) As 264, is an even number it is divisible by 2. Also, the sum of the digits, that is 2 +6 + 4 = 12 is divisible by 3, so the 264 is also divisible by 3. Thus the number 264 is divisible by 6 because it is divisible by 2 and 3 both.

Example 2: Using the divisibility rule of 6, find out whether the number 4578 is divisible by 6 or not.
Solution: As 4578 is an even number it is divisible by 2. Also, the sum of the digits that is 4+ 5+ 7 + 8 = 24 is divisible by 3, or we can add the digits of 24 to make it easy 2 +4 = 6 is divisible by 3, thus, the 4578 is also divisible by 3. Therefore, the number 4578 is divisible by 6 because it is divisible by 2 and 3 (4578 ÷ 6 = 763).

Example 3: Check whether the given large number 433788 is divisible by 6 or not, by using the divisibility rule of 6.
Solution: As the given large number 433788 is an even number (the unit place digit is even) it is divisible by 2. Also, the sum of the digits that is 4+ 3 + 3 + 7 + 8 + 8 = 33 is divisible by 3, or we can add the digits of 33 to make it easy 3 +3 = 6 is divisible by 3, thus, the 433788 is also divisible by 3. Therefore, the number 433788 is divisible by 6 because it is divisible both by 2 and 3. (433788 ÷ 6 = 72298).
FAQs on Divisibility Rule of 6
What is the Divisibility Rule of 6?
The divisibility rule of 6 says that if a number is divisible by 2 and 3 both, then the number is also divisible by 6. For example, 78 is an even number so, it is divisible by 2. The sum of 78 is 15 (7+8=15) and 15 is divisible by 3. Therefore, without doing division we can say that the number 78 is divisible by 6 (78 ÷ 6 = 13) as it is divisible by 2 and 3 both.
Using the Divisibility Rule of 6, Check if 225 is Divisible by 6?
First, we have to check that the number 225 is even or odd. As it is odd that means it is not divisible by 2. Since the number is not divisible by 2, then the number cannot be divisible by 6, because the divisibility rule of 6 states that the number should divisible by 2 and 3 both to make it divisible by 6. So, 225 is not divisible by 6.
What is the Divisibility Rule of 6 and 3?
The divisibility rule of 6 states that the number is exactly divided by number 6 only if it is exactly divided by 2 and 3 both. On the other hand, the divisibility rule of 3 states that if the sum of all digits of a number is divisible by 3 or multiple of 3 then the number is divisible by 3. We use this condition (divisibility rule of 3) in the divisibility test of 6 to check whether a number is divisible by 3 or not, so it is very important to learn the divisibility rule of 3 before learning the divisibility rule of 6.
How do you know if a Big Number is Divisible by 6?
If a big number is divisible by 2 and 3 both then it is also divisible by 6. For this, we need to check whether the unit place digit of the number is even or odd. If it is even then it is divisible by 2. After that, we need to do the sum of all digits and if the sum is divisible by 3 then the number is also divisible by 3. If both the conditions satisfied by the number then without doing division we can say that the number is divisible by 6.
Using the Divisibility Rule of 6, Check if 288 is Divisible by 6?
According to the divisibility rule of 6, the number 288 should be divisible by 2 and 3 both. If it is not, then the number is not divisible by 6. As 288 is an even number it is divisible by 2. The sum of digits is 2+8+8 = 18 and 18 is divisible by 3, thus 288 is divisible by 3. So, yes, 288 is divisible by 6 because it is divisible by 2 and 3 both.
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