Final answer:
The greatest common factor (GCF) of 48 and 12 is 12. This can be found by listing the factors of each number or using prime factorization to identify the largest common factor, which in this case is the number 12 itself.
Step-by-step explanation:
The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. Finding the GCF of 48 and 12 can be done by listing the factors of each number or by using prime factorization.
To list the factors of 48 we have: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. For 12, the factors are: 1, 2, 3, 4, 6, 12. We can see that the greatest factor that these two numbers share is 12.
If we use prime factorization:
- 48 = 2³ × 3¹
- 12 = 2² × 3¹
The common factors are 2² (which is 4) and 3¹ (which is 3), and when we multiply these together we get 4 × 3 = 12
Therefore, the GCF of 48 and 12 is 12.