1. **State the problem:** Find the Highest Common Factor (HCF) of 40 and 50. 2. **Formula and rules:** The HCF of two numbers is the largest number that divides both without leaving a remainder. 3. **Find prime factors:** - 40 = $2^3 \times 5$ - 50 = $2 \times 5^2$ 4. **Identify common prime factors:** Both have at least one 2 and one 5. 5. **Take the lowest powers of common primes:** - For 2: minimum power is 1 - For 5: minimum power is 1 6. **Calculate HCF:** $$\text{HCF} = 2^1 \times 5^1 = 2 \times 5 = 10$$ **Final answer:** The HCF of 40 and 50 is 10.