Final answer:
The GCF and LCM of each pair of numbers can be found by listing the factors and multiples of the numbers respectively.
Step-by-step explanation:
The GCF (Greatest Common Factor) is the largest number that divides evenly into both given numbers. The LCM (Least Common Multiple) is the smallest multiple that both given numbers share in common.
a) For the pair 64 and 240, we can find the GCF by listing the factors of each number and identifying the largest factor they have in common. The factors of 64 are 1, 2, 4, 8, 16, 32, and 64.
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240. The largest factor they have in common is 8, so the GCF is 8.
To find the LCM, we can list the multiples of each number until we find one they both share. The multiples of 64 are 64, 128, 192, 256, ... and the multiples of 240 are 240, 480, 720, 960, ... The smallest multiple they have in common is 960, so the LCM is 960.
b) For the pair 48 and 72, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The largest factor they have in common is 24, so the GCF is 24.
The multiples of 48 are 48, 96, 144, 192, ... and the multiples of 72 are 72, 144, 216, 288, ... The smallest multiple they have in common is 144, so the LCM is 144.