Divisibility Rule of 6

The divisibility rule of 6 states that a number is said to be divisible by 6 if it is divisible by 2 and 3 both. For this, we need to use the divisibility test of 2 and the divisibility test of 3. Divisibility rules help in solving problems easily without actually performing the division. Let us learn more about the divisibility rule of 6 in this article.

A whole number is said to be divisible by 6 if it fulfills the two conditions given below.

• The given whole number should be divisible by 2. A number is divisible by 2 if the digit on the units place of the number is even, i.e., it is 0, 2, 4, 6, and 8.
• The given whole number should be divisible by 3. A number is divisible by 3 if the sum of all digits of the number 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 both the conditions then the given 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.

Divisibility Rule of 6 with Examples

Example: Apply the divisibility test of 6 on the number 9156.

Solution:
Condition 1: The given number should be divisible by 2. Here, 9156 ends with an even number (6). Therefore, it is divisible by 2 [9156 ÷ 2 = 4578]
Condition 2: The given number should 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. Therefore, the number 9156 is divisible by 3.
Since 9156 is divisible by both 2 and 3, we can say that it is divisible by 6.

Example: Apply the divisibility rule of 6 on the number 825.

Solution:
Condition 1: The given number should be divisible by 2. Here, 825 ends with an odd number (5) which means that it is NOT divisible by 2.
Condition 2: The given number should 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, which means that the number 825 is divisible by 3 (825 ÷ 3 = 275)
We can see that 825 is divisible by 3, but it is NOT divisible by 2. Since the number does not meet one condition, therefore, 825 is NOT divisible by 6.

The divisibility rule of 6 is the same for all numbers whether it is a small number or a large number. A large number is divisible by 6 if it is divisible by 2 and 3 both. In other words, a large number should satisfy both the conditions of the divisibility test of 6.

Let us follow the steps given below to check if a large number is divisible by 6 or not.

• Step 1: Observe if the given number is even or odd. This can be done by checking the last digit of the given number which should be even (0, 2, 4, 6, 8). If it is an even number, 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.

Example: Use the divisibility rule of 6 on 145962.

Solution: Let us use the divisibility test of 6 on 145962 with the help of the following steps.

• Step 1: The number 145962 is even, so it is divisible by 2.
• Step 2: The sum of all digits is 1 + 4 + 5 + 9 + 6 + 2 = 27. The sum 27 is divisible by 3 which means 145962 is also divisible by 3.
• Step 3: The number 145962 is divisible by 2 and 3 both. Therefore, the number 145962 is divisible by 6.

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, the number is said to be divisible by 6. The divisibility rule for 7 states that for a number to be divisible by 7, multiply the last digit of the number by 2, and subtract it with the rest of the number to its left leaving the digit at the units place. If the result is either 0 or a multiple of 7, then the number is divisible by 7. For example, let us take the number 443. The number on the last digit is 3. After we multiply it by 2 we get 6 (3 × 2 = 6). Now, let us subtract it from the remaining part of the number which is 44. So, 44 - 6 = 38. But 38 is not divisible by 7, so we can say that 443 is not divisible by 7.

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. Let us check whether 450 is divisible by 6 or not. For this, we first check its divisibility by 2 and 3. The last 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, let us check if 450 is divisible by 9. The divisibility rule says that we need to find the sum of the numbers, which is 4 + 5 + 0 = 9, which is divisible by 9. Hence, 450 is divisible by both 6 and 9.

☛ Related Topics

• Divisibility Rule of 3
• Divisibility Rule of 4
• Divisibility Rule of 5
• Divisibility Rule of 7
• Divisibility Rule of 8
• Divisibility Rule of 9
• Divisibility Rule of 11
• Divisibility Rule of 13

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 said to be 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) because it is divisible by 2 and 3 both.

Using the Divisibility Rule of 6, Check if 225 is Divisible by 6.

The number 225 is not divisible by 6. Using the divisibility test of 6, first, we need to check if the number 225 is even or odd. We can see that 225 is an odd number which means it is not divisible by 2. Since the number is not divisible by 2, it 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 a number is said to be divisible by 6 only if it is completely divisible 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, then the number is divisible by 3. We use the divisibility rule of 3 in the divisibility test of 6, so it is very important to learn the divisibility rule of 3 before learning the divisibility rule of 6.

How to Check the Divisibility by 6 for Large Numbers?

If a large number is divisible by 2 and 3 both, then it is also divisible by 6. For this, we first need to check whether the given number is even or odd. If it is an even number then it is divisible by 2. After that, we need to find the sum of all the digits and if the sum is divisible by 3 then the number is also divisible by 3. Once both the conditions are satisfied, we can say that the number is divisible by 6.

Using the Divisibility Rule of 6, test the Divisibility of the number 288 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. Therefore, we can say that 288 is divisible by 6 because it is divisible by 2 and 3 both.

Write the Divisibility Rule of 6 with Example.

The divisibility rule of 6 states that the given number should be divisible by both 2 and 3. For example, if we take the number 864, we can see that it is divisible by 2 because 864 is an even number. Now, let us check if it is divisible by 3. Since 8 + 6 + 4 = 18, and we know that 18 is divisible by 3. Therefore, the number 864 is divisible by both 2 and 3. This means that the given number 864 is divisible by 6.