I am having some trouble with this problem: What characteristics 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 numbers that have this characteristic. Here is my answer: 8, 10, 15, 26, 33 each have four distinct factions. Another 2 numbers that have this characteristic are: 6 and 27. Did I answer this right? Could you explain it to me if my answer is not right? Thanks.

What do you mean have four distinct "fractions"? Please explain to me how 26 has four distinct "fractions".

This same question has appeared before.

I ignored it at the time since I thought it was a silly question.

Just about as absurd as
"What characteristics do the numbers 2, 3 10 12 12 have that the numbers 1, 4, 5, 6, 7, 8, 9, 11, 14 don't have?"

answer: When sounded out in English the first set starts with the letter "t"

My Lord. And this is in math class? Drop the class, if not drop the school.

Here is my answer: 8, 10, 15, 26, 33 each have four distinct factors. Another 2 numbers that have this characteristic are: 6 and 27. Did I answer this right? Could you explain it to me if my answer is not right? Thanks.

B.B. In my opinion I think your explanation holds water after the minor typo correction. There was a hint about listing the factors. Yes, 6 and 27 both have 4 factors, counting 1 and the number itself.
I was thinking along the same lines in the previous posted question, but since I did not list the factors explicitly, and in my mind, I only counted prime factors, so I missed.

Your answer is partially correct, but there are some errors. To determine the characteristics the numbers have that the others don't have, you are asked to list the factors of each number and compare them.

Let's go through the process to find the correct answer:

Factors are the numbers that divide evenly into another number without leaving a remainder. For example, the factors of 8 are 1, 2, 4, and 8 because these numbers can divide 8 without any remainder.

Now, let's list the factors of each number from the given sets:

For the set {8, 10, 15, 26, 33}:
- The factors of 8 are 1, 2, 4, and 8.
- The factors of 10 are 1, 2, 5, and 10.
- The factors of 15 are 1, 3, 5, and 15.
- The factors of 26 are 1, 2, 13, and 26.
- The factors of 33 are 1, 3, 11, and 33.

For the set {5, 9, 16, 18, 24}:
- The factors of 5 are 1 and 5.
- The factors of 9 are 1, 3, and 9.
- The factors of 16 are 1, 2, 4, 8, and 16.
- The factors of 18 are 1, 2, 3, 6, 9, and 18.
- The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Now, let's compare the lists and find the characteristics that the first set has, which the second set doesn't have:

1. The numbers from the first set have four distinct factors: 8, 10, 15, 26, 33.
2. The numbers from the second set do not have four distinct factors.

So, your answer is correct in stating that the numbers 8, 10, 15, 26, and 33 have four distinct factors. However, your additional numbers, 6 and 27, do not have this characteristic. A possible correct answer for two additional numbers with four distinct factors could be 35 and 39.

To summarize, the correct answer is:

The numbers 8, 10, 15, 26, and 33 each have four distinct factors. Two additional numbers that also have this characteristic are 35 and 39.