What characteristic do the numbers 8, 10, 15, 26, and

33 have that the numbers 5, 9, 16, 18, and 24 don’t
have? (Hint: List the factors of the numbers.) Give two
more numbers that have this characteristic.

To determine the characteristic that the first set of numbers has but the second set does not have, we need to analyze the factors of each number.

Factors are the numbers that can divide a given number evenly without leaving a remainder. To identify the factors of a number, we can systematically divide the number by each integer starting from 1 until the number itself. If there is no remainder, that integer is a factor of the number.

Let's list the factors of each number and compare the two sets:

Factors of 8: 1, 2, 4, 8
Factors of 10: 1, 2, 5, 10
Factors of 15: 1, 3, 5, 15
Factors of 26: 1, 2, 13, 26
Factors of 33: 1, 3, 11, 33

Factors of 5: 1, 5
Factors of 9: 1, 3, 9
Factors of 16: 1, 2, 4, 8, 16
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

From the comparison, we can observe that the numbers in the first set (8, 10, 15, 26, and 33) have an odd number of factors, while the numbers in the second set (5, 9, 16, 18, and 24) have an even number of factors.

The characteristic that distinguishes them is the count of factors. The numbers with an odd number of factors can be expressed as a product of two different prime numbers raised to a power greater than or equal to 1.

To find two more numbers with this characteristic, we can identify numbers that fit this criterion. For example:

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 35: 1, 5, 7, 35

Both 30 and 35 have an odd number of factors and exhibit the same characteristic as the initial set.

Jessica, Chandice, and Thomas or whoever -- please post your attempts to answer these 8 questions.