Divisibility Test: Is 681 Divisible by 6?

Divisibility Rules with Multiple Conditions

Determine if the following number is divisible by 6:

681 681

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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 Based on the ones digit, we know that the number is not divisible by 2
00:08 If the number is not divisible by 2, it is not divisible by 6
00:11 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:

681 681

2

Step-by-step solution

To determine if 681 is divisible by 6, we need to apply the divisibility rules for both 2 and 3:

  • Divisibility by 2: A number is divisible by 2 if its last digit is even. The last digit of 681 is 1, which is odd. Therefore, 681 is not divisible by 2.
  • Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 681 is 6+8+1=15 6 + 8 + 1 = 15 . Since 15 is divisible by 3, 681 meets this condition.

Since 681 is not divisible by 2, even though it is divisible by 3, we conclude that 681 is not divisible by 6.

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 is divisible by 6 only if divisible by both 2 and 3
  • Technique: Check last digit for 2: 681 ends in 1 (odd), so fails
  • Check: Sum of digits 6+8+1=15 6+8+1=15 is divisible by 3, but not by 2 ✓

Common Mistakes

Avoid these frequent errors
  • Only checking divisibility by one factor
    Don't check just divisibility by 3 and conclude the number is divisible by 6 = wrong answer! Both conditions must be met simultaneously. Always verify divisibility by both 2 AND 3 before concluding divisibility by 6.

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

+

Because 6 = 2 × 3, a number must be divisible by both prime factors. If it fails either test, it cannot be divisible by 6. Both conditions are required!

What if a number is divisible by 3 but not by 2?

+

Then it's not divisible by 6! Like 681: it's divisible by 3 but not by 2, so the answer is No. You need both conditions to be true.

Is there a shortcut to check divisibility by 6?

+

No reliable shortcut exists. You must check both the divisibility by 2 rule (even last digit) and the divisibility by 3 rule (sum of digits divisible by 3).

Can a number be divisible by 6 if it's odd?

+

No, never! All numbers divisible by 6 must be divisible by 2, which means they must be even. Odd numbers like 681 cannot be divisible by 6.

How do I remember the divisibility rule for 3?

+

Add up all the digits in the number. If this sum is divisible by 3, then the original number is too! For 681: 6+8+1=15 6+8+1=15 , and 15 ÷ 3 = 5, so 681 is divisible by 3.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Division - Advanced questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations