Introduction:
To find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of two numbers, we will follow a step-by-step process. In this case, we need to find the HCF and LCM of 1224 and 1768.

Step 1: Prime Factorization:
First, we need to find the prime factorization of both numbers.

Prime factorization of 1224:
1224 = 2 * 2 * 2 * 3 * 3 * 17 = 2^3 * 3^2 * 17

Prime factorization of 1768:
1768 = 2 * 2 * 2 * 13 * 17 = 2^3 * 13 * 17

Step 2: HCF Calculation:
To find the HCF, we need to identify the common prime factors of both numbers and multiply them together.

Common prime factors:
2^3 * 17

HCF = 2^3 * 17 = 136

Step 3: LCM Calculation:
To find the LCM, we need to identify the highest power of each prime factor between the two numbers and multiply them together.

Prime factors:
2^3 * 3^2 * 13 * 17

LCM = 2^3 * 3^2 * 13 * 17 = 66,768

Conclusion:
The HCF of 1224 and 1768 is 136, while the LCM is 66,768. The HCF represents the largest number that can divide both 1224 and 1768 without leaving a remainder, while the LCM represents the smallest number that is divisible by both 1224 and 1768. By following the step-by-step process of prime factorization and identifying the common factors, we can easily find the HCF and LCM of any given numbers.

Answer. Step-by-step explanation: H. C. F. :- 17 | 1224, 1768