what is the greatest common factor of 16 and 12
What is the greatest common factor of 16 and 12?
Answer: To find the greatest common factor (GCF) of 16 and 12, follow these steps:
1. Determine the Prime Factorizations
First, determine the prime factorizations of 16 and 12.
-
The prime factorization of 16:
16 = 2^4 -
The prime factorization of 12:
12 = 2^2 \times 3
2. Identify the Common Prime Factors
Next, identify the common prime factors between the two numbers. The common prime factor between 16 and 12 is 2.
3. Take the Lowest Power of Common Prime Factors
Now, take the lowest power of the common prime factor(s).
- Here, the common prime factor is 2.
- The lowest power of 2 in the factorization of 16 is 2^4.
- The lowest power of 2 in the factorization of 12 is 2^2.
Therefore, the GCF is 2^2 = 4.
Conclusion
The greatest common factor of 16 and 12 is \boxed{4}.