Divisibility Test: Is 876 Divisible by 6?

Divisibility Rules with Composite Numbers

Determine if the following number is divisible by 6:

876 876

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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
00:10 Now let's sum the digits and see if the sum is divisible by 3
00:19 The sum is divisible, therefore the number is divisible by 6
00:27 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:

876 876

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Check divisibility by 2.
  • Step 2: Check divisibility by 3.
  • Step 3: Conclude divisibility by 6 based on Steps 1 and 2.

Now, let's work through each step:

Step 1: Check divisibility by 2.
The last digit of 876 is 6, which is an even number. Thus, 876 is divisible by 2.

Step 2: Check divisibility by 3.
The sum of the digits is 8+7+6=218 + 7 + 6 = 21.
Check if 21 is divisible by 3: divide 21÷3=721 \div 3 = 7, which is a whole number. Thus, 21 is divisible by 3, so 876 is also divisible by 3.

Step 3: Conclude divisibility by 6.
Since 876 is divisible by both 2 and 3, it is also divisible by 6.

Therefore, the number 876 is divisible by 6, and the answer to the problem is Yes.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Rule: A number is divisible by 6 if divisible by both 2 and 3
  • Technique: Check last digit for 2, sum digits for 3: 8+7+6=21 8+7+6=21
  • Check: Both conditions met means divisible by 6: 876÷6=146 876 \div 6 = 146

Common Mistakes

Avoid these frequent errors
  • Testing divisibility by 6 directly without checking factors
    Don't try dividing 876 ÷ 6 = 146 right away without using divisibility rules! This wastes time and you might make calculation errors. Always check divisibility by 2 and 3 first using their simple rules.

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 can't I just divide by 6 directly?

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You can, but divisibility rules are faster and prevent errors! Checking if the last digit is even and if digit sum is divisible by 3 takes seconds, while long division takes much longer.

What if the digit sum is large like 21?

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Keep applying the rule! Since 21÷3=7 21 ÷ 3 = 7 with no remainder, 21 is divisible by 3. You can also add again: 2+1=3 2+1=3 , and 3 is clearly divisible by 3.

Do I need to check both 2 and 3 every time?

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Yes, always check both! A number must be divisible by both 2 and 3 to be divisible by 6. Missing either test gives you incomplete information.

What other numbers work like this?

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Any composite number! For example, to check divisibility by 12, test divisibility by both 3 and 4. The key is breaking down the number into its prime factors.

What if a number ends in 0?

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Numbers ending in 0 are automatically divisible by 2 (since 0 is even). You still need to check the digit sum rule for 3 to confirm divisibility by 6.

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