Finding the Odd One Out: Number Properties

The task is to identify the number that doesn't fit the pattern within the list: 3, 13, 17, 23, 33, 67. We need to examine the properties of each number to find the common characteristic and the exception.

Analyzing Each Number

Let's determine the nature of each number in the sequence:

• 3: This number is divisible only by 1 and 3. It is a prime number.
• 13: This number is divisible only by 1 and 13. It is a prime number.
• 17: This number is divisible only by 1 and 17. It is a prime number.
• 23: This number is divisible only by 1 and 23. It is a prime number.
• 33: This number is divisible by 1, 3, 11, and 33. Since it has factors other than 1 and itself (specifically 3 and 11), it is a composite number. We can express this as $33 = 3 \times 11$.
• 67: This number is divisible only by 1 and 67. It is a prime number.

Identifying the Unique Number

By examining the divisibility of the numbers:

• The numbers 3, 13, 17, 23, and 67 are all prime numbers.
• The number 33 stands out as it is the only composite number in the list.

The common property shared by most numbers in the list is being prime. The number 33 does not share this property.

Conclusion

Therefore, the number 33 is the odd one out because it is a composite number, while all other numbers in the list are prime numbers.