Which group names all the whole number factors of a composite number?
A) 2,3,12,24
B) 1,5,10
C) 1,3,5,15
D) 1,31
Not sure if "a composite number" is meant to be the largest composite number of each group. If this is so, then check the factors of the largest number of each group to see if they are all named. For example, the factors of 31 are 1 and 31. So all integer factors are named.
There are two choices where all factors are named, and the other two name all the factors (like D).
However, only one of the choices contains a "composite number" as the largest number, i.e. not a prime.
Can you find it?
To determine the group that names all the whole number factors of a composite number, you need to identify the factors of the given composite number.
A composite number is a number that has more than two factors, meaning it is not a prime number.
Let's analyze the options:
A) 2, 3, 12, 24
B) 1, 5, 10
C) 1, 3, 5, 15
D) 1, 31
To find the factors of a composite number, you need to check which numbers divide it evenly.
For option A, we need to check if 2, 3, 12, and 24 evenly divide the composite number. If they do, then they are factors. However, if any of them do not divide it evenly, they are not factors.
Option A contains 2 and 3, which are possible factors. We also need to check if 12 and 24 divide the composite number evenly.
Next, let's examine option B. It contains 1, 5, and 10. Similarly, we need to check if these numbers divide the composite number evenly.
Moving on to option C, we find the numbers 1, 3, 5, and 15. Again, we need to check if they are factors of the composite number.
Option D includes the numbers 1 and 31. Similarly, we need to determine if they are factors.
To determine the correct group that names all the whole number factors, we should choose the option where all the numbers listed evenly divide the composite number.
In this case, option C, which includes the numbers 1, 3, 5, and 15, names all the whole number factors of the composite number.
Therefore, the answer is:
C) 1, 3, 5, 15
not A, since 6 is not included
not B, since 2 is not included
not D, since 31 is prime
C