1. **State the problem:** Find the highest common factor (HCF) of 70 and 385 using their prime factor trees. 2. **Prime factorization:** - For 70: From the tree, $70 = 2 \times 5 \times 7$ - For 385: From the tree, $385 = 5 \times 7 \times 11$ 3. **Find common prime factors:** The common prime factors of 70 and 385 are 5 and 7. 4. **Calculate HCF:** Multiply the common prime factors: $$\text{HCF} = 5 \times 7 = 35$$ --- 5. **Complete the prime factor trees for 42 and 105:** - For 42: $42 = 2 \times 3 \times 7$ - For 105: $105 = 3 \times 5 \times 7$ 6. **Find the HCF of 42 and 105:** - Common prime factors: 3 and 7 - HCF: $$\text{HCF} = 3 \times 7 = 21$$ --- 7. **Write 105 as the product of its prime factors:** $$105 = 3 \times 5 \times 7$$ 8. **Work out the HCF of 30 and 105:** - Prime factors of 30: $2 \times 3 \times 5$ - Prime factors of 105: $3 \times 5 \times 7$ - Common prime factors: 3 and 5 - HCF: $$\text{HCF} = 3 \times 5 = 15$$