Divisibility Test: Is 673 Divisible by 3?

Divisibility Rules with Sum of Digits

Determine if the following number is divisible by 3:

673 673

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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 3
00:03 A number is divisible by 3 only if the sum of its digits is divisible by 3
00:07 Let's sum its digits and divide by 3
00:15 The sum of digits is not divisible by 3, therefore the number is not divisible by 3
00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine if the following number is divisible by 3:

673 673

2

Step-by-step solution

To determine if 673 is divisible by 3, we must use the divisibility rule for 3, which states that a number is divisible by 3 if the sum of its digits is divisible by 3.

First, we'll calculate the sum of the digits: 6+7+36 + 7 + 3.

Calculating this, we get: 6+7+3=166 + 7 + 3 = 16.

Next, we check if 16 is divisible by 3. Dividing 16 by 3 gives a quotient of 5 and a remainder of 1.

Since 16 is not divisible by 3 (as it leaves a remainder), we conclude that 673 is not divisible by 3.

Thus, the correct answer is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: A number is divisible by 3 if sum of digits is divisible by 3
  • Technique: Add digits: 6+7+3=16 6 + 7 + 3 = 16 , then test 16
  • Check: Since 16 ÷ 3 = 5 remainder 1, then 673 is not divisible by 3 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing the original number instead of testing digit sum
    Don't divide 673 by 3 directly to check divisibility = unnecessary long division! This wastes time and increases error risk. Always add the digits first, then test if that sum divides by 3.

Practice Quiz

Test your knowledge with interactive questions

Determine if the following number is divisible by 3:

\( 564 \)

FAQ

Everything you need to know about this question

Why does adding digits work for divisibility by 3?

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This works because of how our base-10 number system relates to multiples of 3. When you add digits, you're essentially checking if the number leaves the same remainder when divided by 3!

What if the sum of digits is still a big number?

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Keep adding! For example, if digits sum to 27, add again: 2+7=9 2 + 7 = 9 . Since 9 is divisible by 3, the original number is too. Repeat until you get a single digit.

Does this rule work for other numbers like 6 or 9?

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Yes! The digit sum rule works for 3, 6, and 9. For 6, the number must be divisible by both 2 (even) and 3 (digit sum divisible by 3).

How do I quickly tell if 16 is divisible by 3?

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Think of multiples of 3: 3, 6, 9, 12, 15, 18... Since 16 falls between 15 and 18, it's not a multiple of 3. Or divide: 16 ÷ 3 = 5 remainder 1.

Can I use this method for very large numbers?

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Absolutely! This is why the digit sum rule is so powerful. Whether the number has 3 digits or 300 digits, just add all the digits together and test that much smaller sum.

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