Create an Even Number Using 5, 3, 7, 4: A Divisibility Challenge

Even Number Formation with Digit Arrangement

Look at the following digits:

5, 3, 7, 4

Create a number using these digits that results in a whole number when divided by 2.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Compose a number that is divisible by 2
00:04 A number where the ones digit is even is divisible by 2
00:08 According to this method, we'll go through all numbers and eliminate accordingly
00:28 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

Look at the following digits:

5, 3, 7, 4

Create a number using these digits that results in a whole number when divided by 2.

2

Step-by-step solution

To solve this problem, we need to apply the rule of divisibility by 2:

  • A number is divisible by 2 if its last digit is even.

We are given the digits: 5, 3, 7, 4.

Among these digits, the only even digit is 4.

Therefore, to form a number that is divisible by 2, 4 must be the last digit.

From the provided multiple-choice options, we will select the number that ends with 4:

  • Reading each choice, we find that choice 4, "7534," has 4 as the last digit and thus is divisible by 2.

Therefore, the correct number is 7534.

3

Final Answer

7534

Key Points to Remember

Essential concepts to master this topic
  • Rule: A number is even if its last digit is even
  • Technique: Place the only even digit (4) in the units place
  • Check: Last digit is 4, so 7534 ÷ 2 = 3767 ✓

Common Mistakes

Avoid these frequent errors
  • Focusing on all digits instead of just the last one
    Don't check if the sum 5+3+7+4=19 is even = wrong method! Divisibility by 2 only depends on the last digit, not the sum or all digits. Always place the even digit (4) at the end.

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?

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The divisibility rule for 2 states that only the units place determines if a number is even. For example, 1234 is even because it ends in 4, while 1235 is odd because it ends in 5.

What if there are multiple even digits to choose from?

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Any even digit (0, 2, 4, 6, 8) in the last position will work! In this problem, we only have one even digit (4), so it must go at the end.

Can I arrange the other digits in any order?

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Yes! Once you place 4 at the end, you can arrange 5, 3, and 7 in any order for the first three positions. All arrangements like 3574, 5374, or 7534 will be even.

How can I quickly identify even and odd digits?

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Even digits: 0, 2, 4, 6, 8 (divisible by 2)
Odd digits: 1, 3, 5, 7, 9 (not divisible by 2)
In our set {5, 3, 7, 4}, only 4 is even.

What if I accidentally put an odd digit at the end?

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The number will be odd and not divisible by 2. For example, 5437 ends in 7 (odd), so 5437 ÷ 2 = 2718.5, which is not a whole number.

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