Find the H.C.F 632,790,869

Solution:
1. Find the prime factorization of each number:
- 632:
- 632 is divisible by 2: 632 \div 2 = 316
- 316 is divisible by 2: 316 \div 2 = 158
- 158 is divisible by 2: 158 \div 2 = 79
- 79 is a prime number.
- So, the prime factorization of 632 is: 2^3 \times 79

- 790:
- 790 is divisible by 2: 790 \div 2 = 395
- 395 is divisible by 5: 395 \div 5 = 79
- 79 is a prime number.
- So, the prime factorization of 790 is: 2^1 \times 5 \times 79

- 869:
- 869 is divisible by 11: 869 \div 11 = 79
- 79 is a prime number.
- So, the prime factorization of 869 is: 11 \times 79

2. Identify common prime factors:
- All the factorizations have the common prime factor 79.

3. H.C.F is the product of the smallest power of all common prime factors:
- The only common prime factor is 79, and it appears with the smallest power of 1 in all factorizations.

4. Therefore, the H.C.F of 632, 790, and 869 is: 79