Final answer:
To find the number x given the GCF of (x,36) as 4 and LCM of (x,36) as 288, we use the relationship GCF × LCM = x × 36 to calculate and find that x equals 32.
Step-by-step explanation:
The question asks us to find the number x given that the Greatest Common Factor (GCF) of (x,36) is 4 and the Least Common Multiple (LCM) of (x,36) is 288. The relationship between the GCF, LCM, and the numbers in question (here, x and 36) is encapsulated by the formula: GCF(x,36) × LCM(x,36) = x × 36. We are given that the GCF is 4 and the LCM is 288, so we can plug these values into the formula to find x:
4 × 288 = x × 36
To find x, we simply divide both sides by 36:
(4 × 288) / 36 = x
x = (4 × 8) = 32
Hence, the value of x that satisfies both the GCF and LCM conditions is 32.