The goal is to identify the number that is different from the others in the given list: 38, 39, 40, and 36.

Analyzing Number Properties

To find the different number, let's examine the properties of each number:

• 38: It is an even number. Its factors are 1, 2, 19, 38. It is not a perfect square.
• 39: It is an odd number. Its factors are 1, 3, 13, 39. It is not a perfect square. It is divisible by 3.
• 40: It is an even number. Its factors are 1, 2, 4, 5, 8, 10, 20, 40. It is not a perfect square.
• 36: It is an even number. Its factors are 1, 2, 3, 4, 6, 9, 12, 18, 36. It is a perfect square, as it equals \(6 \times 6\) or \(6^2\).

Identifying the Odd One Out

Comparing the properties:

• Three numbers (38, 40, 36) are even, while one (39) is odd. If this were the criteria, 39 would be different.
• Two numbers (39, 36) are divisible by 3, while two (38, 40) are not. This doesn't single out one number.
• However, the number 36 is a perfect square (\(6^2 = 36\)), while 38, 39, and 40 are not perfect squares. This property uniquely identifies 36 as the different number among the options.

Conclusion

The number 36 stands out because it is the only perfect square in the list. Therefore, 36 is the different number.