Short Answer 
To find the Highest Common Factor (HCF) of 28 and 72, perform prime factorization resulting in HCF = 4. The Least Common Multiple (LCM) is calculated from the prime factors yielding LCM = 504.
Step 1: Prime Factorization
Begin by expressing each number as a product of its prime factors. For the numbers 28 and 72, this involves decomposing them into their basic components:
- 28 = 22 ‚à öo 7
- 72 = 23 ‚à öo 32
Step 2: Finding the HCF
To determine the Highest Common Factor (HCF), identify the common prime factors and take the lowest power of each. In our example, the common prime factor is 2, where the minimum exponent is:
- 22
This means HCF(28, 72) = 22 = 4.
Step 3: Finding the LCM
For the Least Common Multiple (LCM), combine all the prime factors using the highest power for each prime found in either number:
- LCM(28, 72) = 23 ‚à öo 32 ‚à öo 7
- Calculating this gives: 504.
Thus, the final results are: HCF = 4 and LCM = 504.