Divisibility Test: Is 999 Divisible by 9?

Q: Does this rule work for other numbers besides 9?

Yes! The digit sum rule also works for divisibility by 3. For other numbers like 2, 4, 5, 6, 8, and 10, you need different rules focusing on the last digits or other patterns.

Q: Can I use this method instead of long division?

Absolutely! The digit sum test is much faster than long division. It's a shortcut that mathematicians discovered to make checking divisibility easier and quicker.

Divisibility Rules with Sum of Digits

Is the number below divisible by 9?

$999$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine if the number is divisible by 9

00:03 A number is divisible by 9 only if the sum of its digits is divisible by 9

00:06 Let's sum its digits and divide by 9

00:09 The sum of digits is divisible by 9, therefore the number is divisible by 9

00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Is the number below divisible by 9?

$999$

Step-by-step solution

To determine if the number 999 is divisible by 9, we will apply the divisibility rule for 9. According to this rule, a number is divisible by 9 if the sum of its digits is divisible by 9.

Let's work through the process:

Step 1: Identify the digits of the number 999. They are 9, 9, and 9.
Step 2: Calculate the sum of these digits: $9 + 9 + 9 = 27$ .
Step 3: Check if the sum (27) is divisible by 9. Since $27 \div 9 = 3$ , and 27 is exactly divisible by 9, the original number 999 is also divisible by 9.

Therefore, according to the divisibility rule, the number 999 is divisible by 9.

The correct answer is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: A number is divisible by 9 if digit sum is divisible by 9
Technique: Add all digits: 9 + 9 + 9 = 27, then check if 27 ÷ 9 = 3
Check: Verify by actual division: 999 ÷ 9 = 111 exactly ✓

Common Mistakes

Avoid these frequent errors

Checking if the last digit is divisible by 9
Don't just look at the last digit (9) and assume divisibility = wrong method! This confuses the rule for divisibility by 2 or 5. Always add ALL digits together and check if that sum is divisible by 9.

Practice Quiz

Test your knowledge with interactive questions

Determine if the following number is divisible by 3:

$$ 352 $$

FAQ

Everything you need to know about this question

Why does adding digits work for checking divisibility by 9?

This works because of how our number system is built! When you write 999, it means $9 \times 100 + 9 \times 10 + 9 \times 1$ . The mathematical property behind this rule ensures the digit sum test always works for 9.

What if the digit sum is still a big number?

Keep adding! For example, if your digit sum is 45, add again: 4 + 5 = 9. If you get 9, 18, 27, 36, etc. (multiples of 9), then the original number is divisible by 9.

Does this rule work for other numbers besides 9?

Yes! The digit sum rule also works for divisibility by 3. For other numbers like 2, 4, 5, 6, 8, and 10, you need different rules focusing on the last digits or other patterns.

Can I use this method instead of long division?

Absolutely! The digit sum test is much faster than long division. It's a shortcut that mathematicians discovered to make checking divisibility easier and quicker.

What if I make an error adding the digits?

Double-check your addition! Write it out: 9 + 9 + 9 = 27. If you're unsure, you can always verify with the actual division: 999 ÷ 9 = 111.

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