Divisibility Rules 3, 6, 9
Do you want to learn faster and more easily?
Learning text on the topic Divisibility Rules 3, 6, 9
Divisibility Rules for 3, 6, 9
In this text, we're going to tackle a very helpful maths shortcut that will make working with numbers much easier. They are called the divisibility rules for 3, 6 and 9, and they are handy tricks for quickly figuring out if a number can be divided evenly by three. Let's dive in and become divisibility detectives!
Divisibility Rule for 3
Divisibility Rule for 3: A number is divisible by 3 if the sum of all its digits is also divisible by 3.
This might sound a bit tricky, but it's actually straightforward. By adding up the digits in a number and checking if that sum can be divided by 3, you can tell if the original number is divisible by 3. This saves you from doing long division!
Divisibility Rule for 3 – Example
Let's take a closer look at how to apply this rule with an example. Imagine we have the number 276 and we want to know if it can be divided evenly by 3.
| Step | Action | Result |
|---|---|---|
| 1. Add the digits | 2 + 7 + 6 | 15 |
| 2. Check the sum | 15 is divisible by 3? | Yes, because 3 × 5 = 15 |
| 3. Apply the rule | Is 276 divisible by 3? | Yes, since the sum (15) is divisible by 3 |
Divisibility Rule for 6
Divisibility Rule for 6: A number is divisible by 6 if it is even (divisible by 2) and the sum of its digits is divisible by 3.
This rule is a two-step check involving both divisibility by 2 and 3. If a number passes both checks, it is divisible by 6.
Divisibility Rule for 6 – Example
Let's apply this rule to the number 132 to determine if it can be divided evenly by 6.
| Step | Action | Result |
|---|---|---|
| 1. Check if even | 132 is even? | Yes, it ends in 2 |
| 2. Add the digits | 1 + 3 + 2 | 6 |
| 3. Check the sum | 6 is divisible by 3? | Yes, because 3 × 2 = 6 |
| 4. Apply the rule | Is 132 divisible by 6? | Yes, since it is even and the sum is divisible by 3 |
Divisibility Rule for 9
Divisibility Rule for 9: A number is divisible by 9 if the sum of all its digits is divisible by 9.
This rule requires just one step similar to that for 3 but with a higher divisibility requirement.
Divisibility Rule for 9 – Example
Consider the number 891 to see if it's divisible by 9.
| Step | Action | Result |
|---|---|---|
| 1. Add the digits | 8 + 9 + 1 | 18 |
| 2. Check the sum | 18 is divisible by 9? | Yes, because 9 × 2 = 18 |
| 3. Apply the rule | Is 891 divisible by 9? | Yes, since the sum (18) is divisible by 9 |
Divisibility Rules for 3, 6, 9 – Practice
Practising applying the rules!
Divisibility Rules for 3, 6, 9 – Summary
Key Learnings from this Text:
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 6 if it is even and the sum of its digits is divisible by 3.
- A number is divisible by 9 if the sum of its digits is divisible by 9.
- These rules are helpful for quickly solving divisibility problems without long calculations.
- Practising these rules with exercises helps reinforce understanding and accuracy in applying them.
Keep practising this rule with different numbers you encounter. Before you know it, you'll be a divisibility expert! Don't forget to check out other cool maths shortcuts and tips on our website and continue practising division.
Divisibility Rules for 3, 6, 9 – Frequently Asked Questions
