Digit Manipulation: Adjusting 5201 to be Divisible by 10 Without Remainder

Q: Why can't I swap 0 with 5 or swap 0 with 2?

Those swaps don't put 0 in the units place! For example, swapping 0 with 5 gives 2501, which still ends in 1. Only putting 0 at the end makes it divisible by 10.

Q: What does 'divisible by 10 with no remainder' actually mean?

It means when you divide by 10, you get a whole number answer with nothing left over. Like $ 5200 ÷ 10 = 520 $ exactly!

Q: What if the problem asked about divisibility by other numbers?

Divisible by 2: Last digit must be even (0, 2, 4, 6, 8)Divisible by 5: Last digit must be 0 or 5Divisible by 10: Last digit must be 0 (combines rules for 2 and 5)

Divisibility Rules with Digit Swapping

$5201$

Change one digit of the number above so that it is divisible by $10$ with no remainder.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Replace a digit so that the number is divisible by 10

00:03 A number divisible by 10 is a number where the ones digit is 0

00:07 Therefore, we will replace the ones digit with 0

00:15 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

$5201$

Change one digit of the number above so that it is divisible by $10$ with no remainder.

Step-by-step solution

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

Step 1: Identify the last digit of the given number.
Step 2: Replace the last digit with 0 to satisfy the divisibility condition for 10.
Step 3: Verify that the new number is divisible by 10.

Now, let's work through each step:
Step 1: The given number is 5201. The last digit here is 1.
Step 2: To make the number divisible by 10, we need to replace the last digit, 1, with 0. So, the new number becomes 5200.
Step 3: Verify: The number 5200 ends in 0, thus confirming that it is divisible by 10.

Therefore, the solution to the problem is to change the last digit '1' in 5201 to '0'. This makes the new number 5200, which is divisible by 10.

Swap 1 with 0

Final Answer

Swap 1 with 0

Key Points to Remember

Essential concepts to master this topic

Rule: A number is divisible by 10 if its last digit is 0
Technique: Change only the units digit: 5201 → 5200 by swapping 1 with 0
Check: Verify the new number ends in 0 and divides evenly by 10 ✓

Common Mistakes

Avoid these frequent errors

Changing digits in wrong positions
Don't change digits in the thousands, hundreds, or tens place = still not divisible by 10! Only the units digit determines divisibility by 10. Always focus on making the last digit equal to 0.

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 can't I swap 0 with 5 or swap 0 with 2?

Those swaps don't put 0 in the units place! For example, swapping 0 with 5 gives 2501, which still ends in 1. Only putting 0 at the end makes it divisible by 10.

What does 'divisible by 10 with no remainder' actually mean?

It means when you divide by 10, you get a whole number answer with nothing left over. Like $5200 ÷ 10 = 520$ exactly!

Are there other ways to make 5201 divisible by 10?

Yes! You could change any digit to make the last digit 0. For example: change 5 to get 0201, or change 2 to get 5001. But the question asks to swap digits, so we need 1 ↔ 0.

How do I quickly check if my answer is correct?

Just look at the last digit! If it's 0, then it's divisible by 10. You can also do a quick division: $5200 ÷ 10 = 520$ (whole number = correct!).

What if the problem asked about divisibility by other numbers?

Divisible by 2: Last digit must be even (0, 2, 4, 6, 8)
Divisible by 5: Last digit must be 0 or 5
Divisible by 10: Last digit must be 0 (combines rules for 2 and 5)

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