1. **State the problem:** Find the greatest common factor (GCF) of 24 and 36 using prime factorization and verify it using the factoring method. 2. **Prime factorization method:** - Prime factorize 24: $$24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3$$ - Prime factorize 36: $$36 = 2 \times 2 \times 3 \times 3 = 2^2 \times 3^2$$ 3. **Find common prime factors:** - Common prime factors are 2 and 3. - Take the lowest powers of these common primes: - For 2: minimum power is $2^2$ - For 3: minimum power is $3^1$ 4. **Calculate GCF:** $$\text{GCF} = 2^2 \times 3 = 4 \times 3 = 12$$ 5. **Verification by factoring method:** - Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 - Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 - Common factors: 1, 2, 3, 4, 6, 12 - Greatest common factor is 12. **Final answer:** The GCF of 24 and 36 is **12**.