Divisibility Test: Is 484 Divisible by 6?

Divisibility Rules with Multiple Conditions

Determine if the following number is divisible by 6:

484 484

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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 6
00:04 According to the ones digit, we know the number is divisible by 2
00:15 Now let's sum the digits and see if the sum is divisible by 3
00:22 The sum is not divisible, therefore the number is not divisible by 6
00:28 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 6:

484 484

2

Step-by-step solution

To determine if the number 484 is divisible by 6, we must confirm that it satisfies both divisibility rules for 2 and 3:

  • Divisibility by 2: A number is divisible by 2 if its last digit is even. The last digit of 484 is 4, which is even. Thus, 484 is divisible by 2.
  • Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. For 484, the sum of the digits is 4+8+4=16 4 + 8 + 4 = 16 . To check divisibility by 3, we evaluate whether 16 is divisible by 3, which it is not.

Since 484 is not divisible by 3, even though it is divisible by 2, it cannot be divisible by 6. Therefore, 484 is not divisible by 6.

In conclusion, the answer to the problem is: No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: For divisibility by 6, check both 2 and 3
  • Technique: Sum digits: 4+8+4=16 4 + 8 + 4 = 16 , then check if divisible by 3
  • Check: Even last digit (4) ✓ but digit sum 16 ÷ 3 = 5.33... ✗

Common Mistakes

Avoid these frequent errors
  • Only checking one divisibility condition
    Don't check just divisibility by 2 and assume the number is divisible by 6 = wrong answer! A number must be divisible by BOTH 2 AND 3 to be divisible by 6. Always verify both conditions completely.

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 do I need to check both 2 and 3 for divisibility by 6?

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Because 6 = 2 × 3, and 2 and 3 are both prime numbers. For a number to be divisible by 6, it must have both 2 and 3 as factors, so both conditions must be met!

What if the digit sum is a large number like 16?

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You can keep applying the rule! Since 16 has digits 1 + 6 = 7, and 7 is not divisible by 3, then 16 (and the original number) is not divisible by 3.

Can a number be divisible by 2 but not by 6?

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Absolutely! Many even numbers aren't divisible by 6. For example: 2, 4, 8, 10, 14, 16, 20, 22... They're all even but not all divisible by 3.

Is there a shortcut to check divisibility by 6?

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Unfortunately, no reliable shortcut exists. You must check both conditions separately: even last digit (for 2) and digit sum divisible by 3. Both must be true!

What if I forget which rule goes with which number?

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  • Divisibility by 2: Last digit is even (0, 2, 4, 6, 8)
  • Divisibility by 3: Sum of all digits is divisible by 3
  • Divisibility by 6: Must satisfy BOTH rules above

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