Divisibility rules enable us to easily determine if a number can be divided evenly by another without performing long division. One particularly useful rule is the divisibility rule for 6. According to this rule, a number is divisible by 6 if it meets two conditions: it must be divisible by both 2 and 3. This article will explain the rule in detail, provide illustrative examples, and offer practice problems to help you understand and apply it effectively.

What is Divisibility?

Divisibility refers to the ability of one number to be evenly divided by another without leaving a remainder. In other words, a number n is divisible by another number d if n divided by d results in a whole number.

Divisibility Rules

Divisibility rules are helpful shortcuts that allow you to determine whether a number can be evenly divided by another number without having to perform full division. These rules simplify the process of checking divisibility and are based on the properties of numbers and their digits.

For example:

• A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
• A number is divisible by 3 if the sum of its digits is divisible by 3.

These rules save time and effort when working with large numbers or performing quick calculations.

Divisibility by 6

Divisibility by 6 involves checking if a given number is divisible by both 2 and 3. Let’s state the rule for divisibility as follows:

Rule for Divisibility by 6

The Divisibility Rule of 6 states that for a number to be divisible by 6, it must satisfy both of the following conditions:

• The number must be divisible by 2.
• The number must be divisible by 3.

If a number satisfies both conditions, then it is divisible by 6.

Methods to Test Divisibility by 6

Since 6 is the product of 2 and 3, a number n is divisible by 6 if and only if it satisfies both the conditions for divisibility by 2 and divisibility by 3.

To determine if a number is divisible by 6, follow these steps:

Step 1. Check divisibility by 2

• The number must end in an even digit (0, 2, 4, 6, or 8).

Step 2. Check divisibility by 3

• The sum of the digits of the number must be divisible by 3.

If both conditions are met, then the number is divisible by 6.

Let’s consider an example for a better explanation.

Example: Check if 342 is divisible by 6.

Solution:

1. Check divisibility by 2: The last digit is 2, which is even, so 342 is divisible by 2.
2. Check divisibility by 3: The sum of the digits is 3 + 4 + 2 = 9. Since 9 is divisible by 3, 342 is also divisible by 3.

Since 342 is divisible by both 2 and 3, it is divisible by 6.

Read More,

• Divisibility Rules
• Divisibility Rule for 3
• Divisibility Rule for 11
• Divisibility Rule for 7

Solved Examples on Divisibility by 6

Example 1: Check if 342 is divisible by 6

Solution:

• Check divisibility by 2: The last digit is 2, which is even, so 342 is divisible by 2.
• Check divisibility by 3: The sum of the digits is 3 + 4 + 2 = 9.

Since 9 is divisible by 3, 342 is also divisible by 3.

Since 342 is divisible by both 2 and 3, it is divisible by 6.

Example 2: Check if 2458 is divisible by 6.

Solution:

• Check divisibility by 2: The last digit is 8, which is even, so 2458 is divisible by 2.
• Check divisibility by 3: The sum of the digits is 2 + 4 + 5 + 8 = 19.
  • Since 19 is not divisible by 3, 2458 is not divisible by 3.

Since 2458 is not divisible by 3, it is not divisible by 6.

Example 3: Check if 748392 is divisible by 6

Solution:

• Check divisibility by 2: The last digit is 2, which is even, so 748392 is divisible by 2.
• Check divisibility by 3: The sum of the digits is 7 + 4 + 8 + 3 + 9 + 2 = 33.

Since 33 is divisible by 3 (33 ÷ 3 = 11), 748392 is also divisible by 3.

Since 748392 is divisible by both 2 and 3, it is divisible by 6.

Example 4: Check if 152637485 is divisible by 6.

Solution:

Check divisibility by 2: The last digit is 5, which is not even, so 152637485 is not divisible by 2.

Since 152637485 is not divisible by 2, it is not divisible by 6, even without checking divisibility by 3.

Practice Problems

Problem 1: Is 4236 divisible by 6?

Problem 2: Is 6458 divisible by 6?

Problem 3: Is 56760 divisible by 6?

Problem 4: Is 89107 divisible by 6?

FAQs on Divisibility Rule of 6

What is the Divisibility Rule for 6?

The Divisibility Rule for 6 states that a number is divisible by 6 if it is divisible by both 2 and 3.

How do you Apply the Divisibility Rule for 6?

To apply the rule, check if the number is divisible by 2 (ends in an even digit) and by 3 (the sum of its digits is divisible by 3). If both conditions are met, the number is divisible by 6.

Why does the Divisibility Rule for 6 work?

The rule works because 6 is the product of 2 and 3. If a number can be evenly divided by both 2 and 3, it can also be divided by 6.

Can the Divisibility Rule for 6 be Used for Very Large Numbers?

Yes, the rule can be applied to any size number, as long as you check its divisibility by both 2 and 3.