1. Problem: Find the HCF (Highest Common Factor) of 12, 14, 19, 25, and 36. 2. The HCF of a set of numbers is the greatest number that divides all of them exactly. 3. Prime factorize each number: - 12 = $2^2 \times 3$ - 14 = $2 \times 7$ - 19 = $19$ (prime) - 25 = $5^2$ - 36 = $2^2 \times 3^2$ 4. Identify common prime factors in all numbers: - 12 and 14 share 2 - 19 is prime and does not share factors with others - 25 has factor 5, not common - 36 shares 2 and 3 with some but not all 5. Since 19 and 25 have no common factors with others except 1, the only common factor for all is 1. 6. Therefore, the HCF of 12, 14, 19, 25, and 36 is 1. Final answer: 1