Final answer:
To find the other number when given the GCF is 9, the LCM is 54, and one of the numbers is 27, we use the relation GCF × LCM = Number1 × Number2. Calculating (9 × 54) / 27 gives us the other number, which is 18.
Step-by-step explanation:
The question involves finding the unknown number when given the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) of two numbers, and one of the numbers itself. The GCF of the two numbers is 9, the LCM is 54, and one of the numbers is 27. To find the other number, we can use the relationship that the product of the GCF and LCM of two numbers is equal to the product of those two numbers. In equation form, this is:
GCF × LCM = Number1 × Number2
Using the given values:
9 × 54 = 27 × Number2
Thus, Number2 = (9 × 54) / 27
To simplify, we can divide both sides by 27:
Number2 = 9 × 2
So, the other number is 18.