Divisibility Test: Is 189 a Multiple of 9?

Q: Does this work for other numbers besides 9?

The digit sum method works for 3 and 9 only. For other numbers like 2, 4, 5, 6, 8, you need different divisibility rules. Each number has its own special trick!

Q: What if I make an error adding the digits?

Double-check your addition! For 189: write it clearly as 1 + 8 + 9. Add step by step: 1 + 8 = 9, then 9 + 9 = 18. Getting the digit sum wrong ruins the whole method.

Q: How can I verify my answer is correct?

You can do the actual division: $ 189 ÷ 9 = 21 $ exactly with no remainder. Or use multiplication: $ 9 \times 21 = 189 $ ✓

Divisibility Rules with Digit Sum Method

Is the number below divisible by 9?

$189$

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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

00:07 Let's sum its digits and divide by 9

00:11 The sum of digits is divisible by 9, therefore the number is divisible by 9

00:15 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?

$189$

Step-by-step solution

To determine if 189 is divisible by 9, we apply the divisibility rule for 9:

Step 1: Calculate the sum of the digits of 189.

The number 189 can be broken down into its digits: 1, 8, and 9. We find the sum of these digits:

$1 + 8 + 9 = 18$

Step 2: Check if the sum, 18, is divisible by 9.

We know that 18 divided by 9 equals 2, which is a whole number, meaning 18 is divisible by 9.

Since the sum of the digits (18) is divisible by 9, it follows that 189 itself is divisible by 9.

Therefore, the number 189 is divisible by 9.

Final Answer: 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: For 189, calculate 1 + 8 + 9 = 18, then check if 18 ÷ 9
Check: Since 18 ÷ 9 = 2 exactly, then 189 is divisible by 9 ✓

Common Mistakes

Avoid these frequent errors

Trying to divide the original number instead of using digit sum
Don't try to divide 189 ÷ 9 in your head = confusion and errors! This makes the problem much harder than needed. Always add the digits first: 1 + 8 + 9 = 18, then check if 18 is divisible by 9.

Practice Quiz

Test your knowledge with interactive questions

Will a number divisible by 6 necessarily be divisible by 3?

FAQ

Everything you need to know about this question

Why does adding digits work for testing divisibility by 9?

This works because of how our number system is built! When you have a number like 189, it's really $1 \times 100 + 8 \times 10 + 9 \times 1$ . Since 100, 10, and all powers of 10 leave remainder 1 when divided by 9, the digit sum rule always works!

What if the digit sum is still a big number?

Keep adding digits! For example, if you get 27, add again: 2 + 7 = 9. If you get a single digit that's divisible by 9 (like 9 itself), then the original number is divisible by 9.

Does this work for other numbers besides 9?

The digit sum method works for 3 and 9 only. For other numbers like 2, 4, 5, 6, 8, you need different divisibility rules. Each number has its own special trick!

What if I make an error adding the digits?

Double-check your addition! For 189: write it clearly as 1 + 8 + 9. Add step by step: 1 + 8 = 9, then 9 + 9 = 18. Getting the digit sum wrong ruins the whole method.

How can I verify my answer is correct?

You can do the actual division: $189 ÷ 9 = 21$ exactly with no remainder. Or use multiplication: $9 \times 21 = 189$ ✓

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