1. **State the problem:** We need to draw the prime factor tree for 90 and then use it along with the prime factorization of 252 to find the highest common factor (HCF) of 90 and 252. 2. **Prime factorization of 252 (given):** $$252 = 2 \times 2 \times 3 \times 3 \times 7 = 2^2 \times 3^2 \times 7$$ 3. **Draw the prime factor tree for 90:** - Start with 90. - Divide by the smallest prime factor: 90 ÷ 2 = 45. - Divide 45 by the smallest prime factor: 45 ÷ 3 = 15. - Divide 15 by the smallest prime factor: 15 ÷ 3 = 5. - 5 is a prime number. So the prime factors of 90 are: $$90 = 2 \times 3 \times 3 \times 5 = 2 \times 3^2 \times 5$$ 4. **Find the HCF:** - List the prime factors of both numbers: - 252: $2^2 \times 3^2 \times 7$ - 90: $2 \times 3^2 \times 5$ - The HCF is the product of the lowest powers of common prime factors. - Common prime factors: 2 and 3. - Lowest power of 2: $2^1$ - Lowest power of 3: $3^2$ Therefore, $$\text{HCF} = 2^1 \times 3^2 = 2 \times 9 = 18$$ 5. **Conclusion:** The highest common factor of 90 and 252 is **18**.