1. **State the problem:** Find the Highest Common Factor (HCF) of 100, 350, and 400. 2. **Formula and rules:** The HCF of numbers is the greatest number that divides all of them without leaving a remainder. One way to find the HCF is by prime factorization. 3. **Prime factorization:** - $100 = 2^2 \times 5^2$ - $350 = 2 \times 5^2 \times 7$ - $400 = 2^4 \times 5^2$ 4. **Find common prime factors with lowest powers:** - Common prime factors are $2$ and $5$ - Lowest power of $2$ among the numbers is $2^1$ - Lowest power of $5$ among the numbers is $5^2$ 5. **Calculate HCF:** $$\text{HCF} = 2^1 \times 5^2 = 2 \times 25 = 50$$ 6. **Answer:** The HCF of 100, 350, and 400 is **50**.