Complete 214_: Ensuring Divisibility by 2

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

214 — 214\text{ }_—

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Step-by-step video solution

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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

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1

Understand the problem

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

214 — 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

Practice Quiz

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Is the number 10 divisible by 4?

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