Complete the Number: Make 512_ Even by Filling the Blank

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

The divisibility rule for 2 is based on place value! Since 10, 100, 1000, etc. are all divisible by 2, only the units digit affects whether the whole number is even or odd.

Q: What makes a digit even?

Even digits are 0, 2, 4, 6, and 8. Odd digits are 1, 3, 5, 7, and 9. If a number ends in an even digit, the entire number is even!

Q: Can I just divide each option by 2 to check?

Yes, but it's much faster to use the divisibility rule! Instead of doing four division problems, just check if the last digit is even. Save division for verification.

Q: What if there were multiple blanks to fill?

You'd still focus on the last digit only! For example, in $ 51\_\_2 $, the number would be even regardless of what fills the middle blanks because it ends in 2.

Divisibility Rules with Single Digit Completion

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

$512\text{ }_—$

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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

00:04 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

00:24 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

$512\text{ }_—$

Step-by-step solution

To solve this problem, we'll identify which digit can be placed in the blank space to make the number divisible by 2.

Step 1: Review the divisibility rule for 2.
A number is divisible by 2 if its last digit is even.

Step 2: Evaluate each possible choice for the blank in $512\_.$

Choice 1: If we fill the blank with 1, the number becomes 5121, which ends with 1, an odd number. This is not divisible by 2.
Choice 2: If we fill the blank with 2, the number becomes 5122, which ends with 2, an even number. This number is divisible by 2.
Choice 3: If we fill the blank with 3, the number becomes 5123, which ends with 3, an odd number. This is not divisible by 2.
Choice 4: If we fill the blank with 5, the number becomes 5125, which ends with 5, an odd number. This is not divisible by 2.

Conclusion: Among all choices, only when the blank is filled with 2, the resulting number 5122 is divisible by 2.

Therefore, the correct answer is $2$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: A number is divisible by 2 if its last digit is even
Technique: Check each option: 5121 (odd), 5122 (even), 5123 (odd), 5125 (odd)
Check: Verify 5122 ÷ 2 = 2561 with no remainder ✓

Common Mistakes

Avoid these frequent errors

Checking divisibility by looking at all digits instead of just the last digit
Don't check if 5+1+2+1=9 is divisible by 2 = wrong method! Divisibility by 2 only depends on the last digit, not the sum of all digits. Always focus only on whether the units digit is even (0, 2, 4, 6, 8).

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 look at the last digit for divisibility by 2?

The divisibility rule for 2 is based on place value! Since 10, 100, 1000, etc. are all divisible by 2, only the units digit affects whether the whole number is even or odd.

What makes a digit even?

Even digits are 0, 2, 4, 6, and 8. Odd digits are 1, 3, 5, 7, and 9. If a number ends in an even digit, the entire number is even!

Can I just divide each option by 2 to check?

Yes, but it's much faster to use the divisibility rule! Instead of doing four division problems, just check if the last digit is even. Save division for verification.

What if there were multiple blanks to fill?

You'd still focus on the last digit only! For example, in $51\_\_2$ , the number would be even regardless of what fills the middle blanks because it ends in 2.

Are there similar rules for other numbers?

Yes! Divisibility by 5 means the last digit is 0 or 5. Divisibility by 10 means the last digit is 0. Each number has its own pattern to memorize.

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