Rearrange 5, 1, 0, 2 to Create a Number Divisible by 10

Divisibility Rules with Digit Arrangement

Rearranged the following numbers to make a number divisible by 10:

5, 1 ,0, and 2.

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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 10
00:03 Replace one digit so that the number is divisible by 4
00:08 Using this method, we will go through all numbers and eliminate accordingly
00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Rearranged the following numbers to make a number divisible by 10:

5, 1 ,0, and 2.

2

Step-by-step solution

To solve this problem, we should organize the given digits to make a number that is divisible by 10. According to the rule of divisibility by 10, a number must end in 0.

Let's follow these steps:

  • Step 1: Ensure the number ends in 0 by placing 0 at the unit's place.
  • Step 2: Arrange the remaining digits (5, 1, and 2) to form the largest possible number.
  • Step 3: Arrange 5, 1, and 2 in descending order, resulting in 521.
  • Step 4: Combine the arranged digits with 0 at the end: This gives 5210.

The number 5210 ends with 0, making it divisible by 10.

Therefore, the solution to the problem is 5120 5120 .

3

Final Answer

5120

Key Points to Remember

Essential concepts to master this topic
  • Rule: Numbers divisible by 10 must end in 0
  • Technique: Place 0 last, then arrange remaining digits 5,1,2
  • Check: Verify 5210 ends in 0 and equals given digits ✓

Common Mistakes

Avoid these frequent errors
  • Not placing 0 at the end
    Don't put 0 in the middle like 5021 = not divisible by 10! Numbers divisible by 10 must end in 0, not contain 0 anywhere. Always place 0 as the last digit to ensure divisibility by 10.

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 the number have to end in 0?

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The divisibility rule for 10 states that any number ending in 0 is divisible by 10. This is because 10 = 2 × 5, and ending in 0 guarantees the number has factors of both 2 and 5.

What if I want the smallest number instead of the largest?

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For the smallest number divisible by 10, place 0 at the end and arrange the remaining digits in ascending order. With digits 5,1,2,0, the smallest would be 1250.

Can I put 0 at the beginning?

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Never start with 0! Numbers cannot begin with 0 (like 0521) because that would make it a 3-digit number, not a 4-digit number using all given digits.

How do I arrange the other digits?

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After placing 0 at the end, arrange the remaining digits based on what you want: largest number = descending order (5,2,1), smallest number = ascending order (1,2,5).

Are there other numbers I can make that are divisible by 10?

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Yes! Any arrangement of 5,1,2 followed by 0 works:

  • 5210 ✓
  • 5120 ✓
  • 2510 ✓
  • 2150 ✓
  • 1520 ✓
  • 1250 ✓

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