Final answer:
The GCF is 2x2, and the LCM is 2x2x5x8. Given one number is 32, we use the relationship GCF × LCM = Product of the two numbers to find that the other number is 20.
Step-by-step explanation:
The greatest common factor (GCF) of two numbers is 2x2, and the least common multiple (LCM) of the same two numbers is 2x2x5x8. Given that one number is 32, we want to find the other number. To do this, we can use the relationship between the GCF, LCM, and the two numbers, which is given by:
GCF × LCM = Product of the two numbers
Since we're given that the other number is 32, and we have the GCF and LCM, we can solve for the unknown number:
2x2 (GCF) × 2x2x5x8 (LCM) = 32 × other number
Now, simplify and calculate:
4 (GCF) × 160 (LCM) = 32 × other number
640 = 32 × other number
To find the other number, divide 640 by 32:
other number = 640 / 32
other number = 20
Therefore, the other number is 20.