what is the greatest common factor of 12 and 16
What is the greatest common factor (GCF) of 12 and 16?
Answer: To find the greatest common factor (GCF) of 12 and 16, follow these steps:
1. Prime Factorization:
- Find the prime factorization of each number:
- Prime factorization of 12:
12 = 2^2 \times 3- Prime factorization of 16:
16 = 2^4
2. Identify the Common Factors:
- Both 12 and 16 have the common prime factor of 2.
3. Find the Lowest Powers of Common Prime Factors:
- For the prime factor 2, the lowest power common to both factorizations is 2^2 (since 2 is raised to the power of 2 in 12 and to the power of 4 in 16).
4. Calculate the Greatest Common Factor (GCF):
- Multiply the common factors with their lowest powers:\text{GCF} = 2^2 = 4
Therefore, the greatest common factor (GCF) of 12 and 16 is \boxed{4}.
This method ensures you correctly identify and utilize the greatest common prime factors shared between the two numbers, resulting in their greatest common factor.