Final answer:
To find the GCF and LCM of each pair of numbers, one can use prime factorization, and for pairs such as 36 and 45, the GCF is 9 and the LCM is 180. Similar methods can be applied to the other pairs to determine their GCF and LCM.
Step-by-step explanation:
To find the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) of pairs of numbers, you can use different methods, including prime factorization, listing multiples or factors, and using the formula GCF × LCM = Product of the numbers.
GCF and LCM of 36 and 45
Prime factorization of 36: 2² × 3²
Prime factorization of 45: 3² × 5
GCF: Multiply the lowest powers of all common prime factors: GCF = 3² = 9
To find the LCM, we can multiply the GCF by the non-common factors in both numbers: LCM = GCF × 2² × 5 = 9 × 4 × 5 = 180
Step-by-Step Explanation for Other Pairs
You can apply the same method to the other pairs of numbers mentioned to find their GCF and LCM.
For example, let's determine the GCF and LCM for one more pair:
GCF and LCM of 30 and 75
Prime factorization of 30: 2 × 3 × 5
Prime factorization of 75: 3 × 5²
GCF: Multiply the lowest powers of all common prime factors: GCF = 3 × 5 = 15
LCM: LCM = GCF × 2 × 5 = 15 × 2 × 5 = 150
The steps for pairs c), d), and e) would follow the same process, altering the numbers as necessary.