Find the HCF and LCM of 6, 72, and 120 using the prime factorization method.

To find the highest common factor (HCF) and least common multiple (LCM) of the given numbers (6, 72, and 120) using the prime factorization method, we need to first find the prime factorization of each number.

Prime factorization of 6:
6 = 2 × 3

Prime factorization of 72:
72 = 2 × 2 × 2 × 3 × 3

Prime factorization of 120:
120 = 2 × 2 × 2 × 3 × 5

Now, we can find the HCF by selecting the common prime factors with the lowest exponent:

HCF = 2 × 3 = 6

To find the LCM, we need to select the highest power of each prime factor:

LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360

Therefore, the HCF of 6, 72, and 120 is 6, and the LCM is 360.