1. **State the problem:** Find the highest common factor (HCF) of 56 and 84. 2. **Formula and rules:** The HCF of two numbers is the largest number that divides both without leaving a remainder. One way to find it is by prime factorization or using the Euclidean algorithm. 3. **Prime factorization:** - 56 = $2^3 \times 7$ - 84 = $2^2 \times 3 \times 7$ 4. **Find common factors:** - Common prime factors are $2$ and $7$. - Take the lowest powers: $2^2$ and $7^1$. 5. **Calculate HCF:** $$\text{HCF} = 2^2 \times 7 = 4 \times 7 = 28$$ 6. **Explanation:** The HCF is the product of the prime factors common to both numbers with the smallest exponent. **Final answer:** The HCF of 56 and 84 is 28.