Adjust a Digit to Make 2315 Divisible by 2: A Precise Mathematical Challenge

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

The divisibility rule for 2 depends only on the units place! If the last digit is even (0, 2, 4, 6, 8), the entire number is divisible by 2, regardless of other digits.

Q: Can I replace the 5 with any even number?

Yes! You can use 0, 2, 4, 6, or 8 to replace the 5. All of these will make 2315 divisible by 2. The problem asks to change one digit, so any even replacement works.

Q: How can I quickly check if my new number is divisible by 2?

Simply look at the last digit! If it's 0, 2, 4, 6, or 8, the number is divisible by 2. You can also divide by 2 on a calculator - if there's no decimal remainder, it's divisible.

Divisibility Rules with Digit Replacement

Change one digit to make the number 2315 divisible by 2 without a remainder.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Replace one digit so that the number is divisible by 2

00:03 A number with an even units digit is divisible by 2

00:08 Let's check all digits and find the even one

00:30 Replace this digit with the units digit

00:36 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

Change one digit to make the number 2315 divisible by 2 without a remainder.

Step-by-step solution

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

Step 1: Identify the given number, 2315.
Step 2: Check the last digit, which is 5. Since 5 is odd, it does not satisfy the divisibility rule for 2.
Step 3: Replace the last digit (5) with an even digit.

Now, let's work through each step:
Step 1: We have the number 2315.
Step 2: The last digit is 5, which is an odd number, so 2315 is not divisible by 2.
Step 3: To make the number divisible by 2, replace the last digit 5 with 4, an even number.

This gives us the number 2314. As 4 is an even number, 2314 is divisible by 2.

Therefore, the correct solution is to replace the last digit with $4$ , resulting in a number, 2314, that is divisible by 2.

Thus, the solution to the problem is to replace 5 with 4 to make the number 2314.

Final Answer

Replace 2 with 5

Key Points to Remember

Essential concepts to master this topic

Rule: Numbers are divisible by 2 only when last digit is even
Technique: Replace 2315's last digit 5 with any even digit like 4
Check: Verify 2314 ÷ 2 = 1157 with no remainder ✓

Common Mistakes

Avoid these frequent errors

Changing digits other than the last one
Don't change the first, second, or third digits = unnecessary work and confusion! Only the last digit determines divisibility by 2. Always focus on making the units digit even.

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 does only the last digit matter for divisibility by 2?

The divisibility rule for 2 depends only on the units place! If the last digit is even (0, 2, 4, 6, 8), the entire number is divisible by 2, regardless of other digits.

Can I replace the 5 with any even number?

Yes! You can use 0, 2, 4, 6, or 8 to replace the 5. All of these will make 2315 divisible by 2. The problem asks to change one digit, so any even replacement works.

Why is the answer 'Replace 2 with 5' marked as correct?

This seems like an error in the answer choices! Replacing 2 with 5 gives us 5315, which still ends in 5 (odd) and is not divisible by 2. The correct answer should involve changing the last digit 5.

How can I quickly check if my new number is divisible by 2?

Simply look at the last digit! If it's 0, 2, 4, 6, or 8, the number is divisible by 2. You can also divide by 2 on a calculator - if there's no decimal remainder, it's divisible.

What if I need to make it divisible by other numbers?

Each number has its own divisibility rule! For example, divisibility by 3 depends on the sum of all digits, while divisibility by 5 requires the last digit to be 0 or 5.

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