Arrange 2, 1, and 3: Formulating a Number Divisible by 2

Divisibility Rules with Digit Arrangements

Rearrange the following digits to create a number divisible by 2:

2, 1, and 3.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Create a number that is divisible by 2
00:04 A number where the ones digit is even is divisible by 2
00:09 According to this method, we will go through all numbers and eliminate accordingly
00:42 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Rearrange the following digits to create a number divisible by 2:

2, 1, and 3.

2

Step-by-step solution

To solve this problem, let's explore how to form a number divisible by 2 using the digits 2, 1, and 3. A number is divisible by 2 if the last digit is an even number, which, from our given digits, is only the digit 2.

Let's examine all possible permutations of these digits and identify which numbers are divisible by 2:

  • Permutation 1: 213, where the last digit is 3 (not divisible by 2).
  • Permutation 2: 231, where the last digit is 1 (not divisible by 2).
  • Permutation 3: 123, where the last digit is 3 (not divisible by 2).
  • Permutation 4: 132, where the last digit is 2 (divisible by 2).
  • Permutation 5: 312, where the last digit is 2 (divisible by 2).
  • Permutation 6: 321, where the last digit is 1 (not divisible by 2).

From our examination, the numbers 132 and 312 both end in 2, making them divisible by 2. Therefore, the correct choice according to the problem's options is to select both permutations that satisfy the condition.

Therefore, the solution to the problem is Answer b and c.

3

Final Answer

Answer b and c.

Key Points to Remember

Essential concepts to master this topic
  • Rule: A number is divisible by 2 if last digit is even
  • Technique: Check all arrangements: 132 and 312 end in 2
  • Check: Verify even last digit: 132 ÷ 2 = 66 and 312 ÷ 2 = 156 ✓

Common Mistakes

Avoid these frequent errors
  • Only checking if the digits themselves are even
    Don't think 2 is even so any arrangement works = wrong answer! The position matters, not just having an even digit. Always check that the last digit (units place) is even for divisibility 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?

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The divisibility rule for 2 depends on place value! Only the units place determines if a number is even or odd. For example, 321 has even digit 2, but it's odd because it ends in 1.

Do I need to check all possible arrangements?

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Yes! With digits 1, 2, 3, there are 6 possible arrangements: 123, 132, 213, 231, 312, 321. List them systematically to avoid missing any.

What if I have more digits to arrange?

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The same rule applies! Focus on arrangements that end in even digits. With digits 1, 2, 3, 4, you'd look for numbers ending in 2 or 4.

Can a number be divisible by 2 if it contains odd digits?

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Absolutely! Numbers like 132 and 518 are divisible by 2 even though they contain odd digits. Only the last digit needs to be even (0, 2, 4, 6, or 8).

How do I remember the divisibility rule for 2?

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Think of it as the "even ending" rule! If a number ends in an even digit (0, 2, 4, 6, 8), it's divisible by 2. This is the same as asking "Is this number even or odd?"

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