Complete 214_: Ensuring Divisibility by 2

Q: Why do I only need to check the last digit for divisibility by 2?

The divisibility rule for 2 is based on place value! Since every place value position except the units place represents an even number of something (tens, hundreds, etc.), only the units digit determines if the whole number is even or odd.

Q: What makes a digit 'even'?

Even digits are 0, 2, 4, 6, and 8. These digits can be divided by 2 with no remainder. Odd digits are 1, 3, 5, 7, and 9.

Q: What if the problem asked for divisibility by 5 instead?

For divisibility by 5, the number must end in 0 or 5. Each divisibility rule has its own pattern - that's why it's important to memorize the key ones!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the digit so that the number is divisible by 2

00:03 A number where the ones digit is even is divisible by 2

00:08 According to this method, we will go through all numbers and eliminate accordingly

00:26 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

Complete the numbers to obtain a number divisible by 2 without remainder.

$214\text{ }_—$

2

Step-by-step solution

1. The problem is asking to fill in the blank in the number 214_ with a single digit so that the complete number is divisible by 2. 2. To determine divisibility by 2, the number must end in an even digit (0, 2, 4, 6, or 8). 3. We will evaluate the given choices to see which digits can complete the number to meet this criteria. 4. The rule for divisibility by 2 states that if a number ends in an even digit, it is divisible by 2. 5. We will check each provided option to confirm divisibility. 6. Steps include checking if the number formed with each potential digit is divisible by 2. 7. Assumptions: None required beyond the divisibility rule itself. 8. This is a straightforward application of the divisibility rule; no complex decomposition is necessary. 9. There are no special conditions; any even number from the provided choices will suffice. 10. Review each choice to see if it fits, confirming there is no required explanation of incorrect options as per instructions. 11. Compare each choice against the divisibility rule. 12. Common mistakes might include not understanding the even number criteria. 13. Changing the last digit affects whether the number is even and hence divisible by 2.

To solve this problem, we need to ensure that the complete number is divisible by 2. According to the rules of divisibility for 2, a number is divisible by 2 if its last digit is even. Therefore, we need to select a digit to replace the blank that will result in an even number when appended to 214.

Let's evaluate the provided choices:

Choice 1: 2144 – The number ends in 4, which is even. So, 2144 is divisible by 2.
Choice 2: 2146 – The number ends in 6, which is even. So, 2146 is divisible by 2.
Choice 3: 2148 – The number ends in 8, which is even. So, 2148 is divisible by 2.
Choice 4: "All answers are correct" – Since all proposed numbers (2144, 2146, 2148) end in even digits, they are each divisible by 2.

Based on these evaluations, all individual choices result in a number that is divisible by 2.

Therefore, the correct answer is: All answers are correct.

3

Final Answer

All answers are correct

Key Points to Remember

Essential concepts to master this topic

Rule: A number is divisible by 2 if it ends in an even digit
Technique: Check last digit: 2144, 2146, 2148 all end in even numbers
Check: Verify divisibility: 2144 ÷ 2 = 1072, 2146 ÷ 2 = 1073, 2148 ÷ 2 = 1074 ✓

Common Mistakes

Avoid these frequent errors

Checking the whole number instead of just the last digit
Don't divide 214_ by 2 to test divisibility = unnecessary work and confusion! You only need to look at the units digit. Always check if the last digit is 0, 2, 4, 6, or 8 to determine divisibility by 2.

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 do I only need to check the last digit for divisibility by 2?

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The divisibility rule for 2 is based on place value! Since every place value position except the units place represents an even number of something (tens, hundreds, etc.), only the units digit determines if the whole number is even or odd.

What makes a digit 'even'?

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Even digits are 0, 2, 4, 6, and 8. These digits can be divided by 2 with no remainder. Odd digits are 1, 3, 5, 7, and 9.

Can there be more than one correct answer for this type of problem?

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Yes! Any even digit that completes the number will make it divisible by 2. In this case, 4, 6, and 8 all work, so all answers are correct.

How can I quickly check if my answer is right?

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Simply look at the last digit of your completed number. If it's 0, 2, 4, 6, or 8, then the number is divisible by 2. No calculation needed!

What if the problem asked for divisibility by 5 instead?

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For divisibility by 5, the number must end in 0 or 5. Each divisibility rule has its own pattern - that's why it's important to memorize the key ones!

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Complete 214_: Ensuring Divisibility by 2

Divisibility Rules with Even Numbers

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