Construct an Even Number: Divisibility Test with 8, 1, 3, 7

Even Number Formation with Given Digits

Look at the following digits:

8, 1, 3, 7

Create a number using these digits that results in a whole number when divided by 2.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Compose a number that is divisible by 2
00:04 A number where the ones digit is even is divisible by 2
00:09 According to this method, we will go through all numbers and eliminate accordingly
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

Look at the following digits:

8, 1, 3, 7

Create a number using these digits that results in a whole number when divided by 2.

2

Step-by-step solution

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

  • Step 1: Identify and understand the requirement for divisibility by 2.
  • Step 2: Determine the potential numbers by rearranging the digits to satisfy the divisibility rule.
  • Step 3: Confirm by checking the last digit of the arranged number.

Now, let's work through each step:
Step 1: A number is divisible by 2 if its last digit is even. Among the given digits (8, 1, 3, 7), only 8 is even.
Step 2: Rearrange the digits so that the last digit is 8. Potentially, using all digits, the number 1378 can be formed.
Step 3: Check that 1378 ends with 8, confirming it is divisible by 2.

Therefore, the solution to the problem is 1378.

3

Final Answer

1378

Key Points to Remember

Essential concepts to master this topic
  • Divisibility Rule: A number is divisible by 2 if its last digit is even
  • Technique: Place the only even digit (8) at the end: 1378
  • Check: Verify the last digit is even and divide: 1378 รท 2 = 689 โœ“

Common Mistakes

Avoid these frequent errors
  • Placing an odd digit at the end
    Don't put 1, 3, or 7 as the last digit = odd number that's not divisible by 2! This violates the fundamental rule that even numbers must end in 0, 2, 4, 6, or 8. Always identify which digits are even first, then place an even digit at the end.

Practice Quiz

Test your knowledge with interactive questions

Is the number 43 divisible by 4?

FAQ

Everything you need to know about this question

Why can't I use 7813 or 3781 if they use all the same digits?

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The order matters for divisibility! Even though these numbers use the same digits, they end with odd numbers (3 and 1), making them odd numbers that aren't divisible by 2.

What if there were multiple even digits to choose from?

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You could place any of the even digits at the end! For example, with digits 2, 4, 6, 8, you could make 2468, 4682, 6824, or many other combinations - all would be divisible by 2.

Do I need to use all the given digits?

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Yes! The problem asks you to create a number using these digits, which typically means using each digit exactly once to form a complete number.

How can I quickly identify even digits?

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Even digits are: 0, 2, 4, 6, 8. Odd digits are: 1, 3, 5, 7, 9. In this problem, only 8 is even among the given digits 8, 1, 3, 7.

What's the easiest way to check if my answer is correct?

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Look at the last digit of your number. If it's 0, 2, 4, 6, or 8, then your number is even and divisible by 2. You can also divide by 2 to double-check!

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