Use effective reasoning to determine the composite number described.(1 point)

Question

I am a composite number. I am greater than 16, but less than 20. Two of my factors are a number and the number doubled. I am the number

Answer 1

To identify the composite number based on the given criteria, let's analyze the clues step by step:

1. Composite Number: A composite number has more than two factors, meaning it can be divided evenly by numbers other than 1 and itself.

2. Range: The number must be greater than 16 and less than 20. The whole numbers in this range are 17, 18, and 19.

3. Factors: The clue states that two of the number's factors are a number \( n \) and \( n \) doubled (which is \( 2n \)). For these to be factors of the composite number, the number must be able to be expressed as \( n \times m \) where \( n \) and \( 2n \) are both factors.

Now let's analyze the numbers between 17 and 20:

• 17: This is a prime number, so it cannot be composite.
• 18: The factors of 18 are 1, 2, 3, 6, 9, 18. We can see that 2 (which is \( n \)) and 4 (which is \( 2n \)) fit here, as \( n = 2 \) leads to \( 2n = 4\), but since 4 is not a factor of 18, we cannot conclude.
• 19: This is a prime number, hence, it cannot be composite.

From this analysis, the only number that fits all conditions is 18.

Thus, the composite number you are referring to is 18.