Complete 105_ for Divisibility by 2: Find the Missing Digit

Q: Why does only the last digit matter for divisibility by 2?

Because place values work like this: every position except the units place represents multiples of 10, 100, 1000, etc. Since all these are already divisible by 2, only the units digit determines if the whole number is even or odd!

Q: What are all the even digits I can use?

The even digits are 0, 2, 4, 6, and 8. Any of these in the units place makes the entire number divisible by 2. In this problem, only 8 was given as an option.

Q: Do I need to do the actual division to check?

No! You don't need to calculate $ 1058 ÷ 2 $. Just seeing that 8 is even tells you immediately that 1058 is divisible by 2. The divisibility rule is a shortcut!

Q: What if multiple answer choices were even digits?

Then any of the even digits would be correct! This problem only had one even option (8), but if both 2 and 8 were choices, both would make the number divisible by 2.

Q: Does this rule work for really big numbers too?

Yes! Whether it's $ 1058 $ or $ 123,456,788 $, you only need to look at the very last digit. If it's even, the entire number is divisible by 2, no matter how long it is!

Divisibility Rules with Missing Digits

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

$105\text{ }_—$

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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

00:07 According to this method, we will go through all numbers and eliminate accordingly

00:31 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.

$105\text{ }_—$

Step-by-step solution

To solve this problem, we need to apply the rule of divisibility by 2, which states that a number is divisible by 2 if its last digit is an even number.

Let's consider the possible digits for the underscore: $1$ , $5$ , $3$ , and $8$ .

If we insert $1$ , the number becomes $1051$ , which ends in an odd digit, not divisible by 2.
If we insert $5$ , the number becomes $1055$ , which ends in an odd digit, not divisible by 2.
If we insert $3$ , the number becomes $1053$ , which ends in an odd digit, not divisible by 2.
If we insert $8$ , the number becomes $1058$ , which ends in an even digit, divisible by 2.

Since the correct last digit that makes the number divisible by 2 is an even number, the solution to the problem is inserting $8$ .

Therefore, the solution to the problem is $8$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: A number is divisible by 2 if last digit is even
Technique: Check each option: 1051, 1055, 1053, 1058 - only 8 is even
Check: Verify 1058 ÷ 2 = 529 with no remainder ✓

Common Mistakes

Avoid these frequent errors

Checking if the entire number is even instead of just the last digit
Don't look at whether 105 is even = wrong focus on middle digits! Divisibility by 2 only depends on the units place digit. Always check only the last digit - if it's 0, 2, 4, 6, or 8, the whole number is divisible by 2.

Practice Quiz

Test your knowledge with interactive questions

Is the number 10 divisible by 4?

FAQ

Everything you need to know about this question

Why does only the last digit matter for divisibility by 2?

Because place values work like this: every position except the units place represents multiples of 10, 100, 1000, etc. Since all these are already divisible by 2, only the units digit determines if the whole number is even or odd!

What are all the even digits I can use?

The even digits are 0, 2, 4, 6, and 8. Any of these in the units place makes the entire number divisible by 2. In this problem, only 8 was given as an option.

Do I need to do the actual division to check?

No! You don't need to calculate $1058 ÷ 2$ . Just seeing that 8 is even tells you immediately that 1058 is divisible by 2. The divisibility rule is a shortcut!

What if multiple answer choices were even digits?

Then any of the even digits would be correct! This problem only had one even option (8), but if both 2 and 8 were choices, both would make the number divisible by 2.

Does this rule work for really big numbers too?

Yes! Whether it's $1058$ or $123,456,788$ , you only need to look at the very last digit. If it's even, the entire number is divisible by 2, no matter how long it is!

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