Divisibility Test: Is 987 a Multiple of 9?

Divisibility Rules with Sum of Digits

Is the number below divisible by 9?

987 987

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's see if this number can be divided by 9.
00:07 Remember, a number is divisible by 9 if the sum of its digits is also divisible by 9.
00:13 So, let's add up those digits and then check if our total can be divided by 9.
00:21 Hmm, the sum of the digits can't be divided by 9. So, the original number isn't divisible by 9.
00:28 And that's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Is the number below divisible by 9?

987 987

2

Step-by-step solution

To determine if 987 is divisible by 9, we use the divisibility rule that a number is divisible by 9 if the sum of its digits is also divisible by 9.

Let's follow these steps:

  • Step 1: Find the sum of the digits of 987.

We have the digits 9, 8, and 7. Therefore, their sum is:

9+8+7=24 9 + 8 + 7 = 24

  • Step 2: Check if the sum, 24, is divisible by 9.

We divide 24 by 9:

24÷92.67 24 \div 9 \approx 2.67

Since 24 does not evenly divide by 9 (it does not result in an integer), 24 is not divisible by 9.

Thus, since the sum of the digits (24) is not divisible by 9, the number 987 is not divisible by 9.

Therefore, the solution to the problem is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: A number divides by 9 when its digit sum divides by 9
  • Technique: Add digits: 9 + 8 + 7 = 24, then check 24 ÷ 9
  • Check: 24 ÷ 9 = 2.67 (not whole), so 987 is not divisible by 9 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing the original number instead of checking digit sum
    Don't divide 987 ÷ 9 directly to test divisibility = waste of time and harder calculation! The divisibility rule saves work by using smaller numbers. Always add the digits first, then check if that sum divides 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 testing divisibility by 9?

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This works because of how our base-10 number system relates to 9. When you add digits, you're finding the remainder when divided by 9. It's a mathematical shortcut that always works!

What if the digit sum is still a big number?

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Keep adding! If you get 24, you can add again: 2+4=6 2 + 4 = 6 . Since 6 isn't divisible by 9, neither is the original number. Keep going until you get a single digit.

Does this trick work for other numbers besides 9?

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Yes! The digit sum test works for 3 and 9. For 3, if the digit sum divides by 3, so does the original number. Try it with different examples!

How do I know if a number divides evenly?

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A number divides evenly if there's no remainder - the result is a whole number. 24÷9=2.67 24 ÷ 9 = 2.67 has a decimal, so it doesn't divide evenly.

Can I use a calculator to check 24 ÷ 9?

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Absolutely! Calculators help verify your work. If you get a decimal result, the division isn't even. You can also think: 9 × 2 = 18, and 24 - 18 = 6, so there's a remainder.

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