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.
Don't 8, 10, 15, 26, and 33 each have only 4 factors? (i.e., 1, 8, 2, 4)
The others have more or less than 4 factors.
To determine the characteristic that the numbers 8, 10, 15, 26, and 33 have that the numbers 5, 9, 16, 18, and 24 don't have, we can examine the factors of these numbers.
Factors are the numbers that can be evenly divided into a given number. To find the factors of a number, we divide that number by all positive integers less than or equal to its square root. If the remainder is zero, then that number is a factor.
Let's find the factors for each of the numbers given:
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
Now, let's compare them to the second set of numbers:
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 this analysis, we can observe that the characteristic the numbers 8, 10, 15, 26, and 33 have that the other set of numbers don't have is that they have factors other than 1 and themselves.
To find two more numbers with this characteristic, we can consider numbers with more than two factors. For example:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 20: 1, 2, 4, 5, 10, 20
Hence, the numbers 12 and 20 also have the characteristic of having factors other than 1 and themselves.