What is the greatest common factor of 4k, 18k^4, and 12?

To find the greatest common factor (GCF) of the numbers 4k, 18k⁴, and 12, we first need to identify the factors of each term.

1. **Factors of 4k**: The factors are 4 and k. The number 4 can be broken down into its prime factors as 2².

2. **Factors of 18k⁴**: The number 18 can be factored into 2 and 3². So, the factors of 18k⁴ are 2, 3, and k⁴.

3. **Factors of 12**: The prime factorization of 12 is 2² × 3.

Next, we summarize the common factors:

• Common numerical factors from 4, 18, and 12: The common factor is 2 and the smallest power of 2 is 2¹. The other common factor is 3, but only appears in 18 and 12, not in 4.

Now, we combine the common numerical factor:

The GCF of the numerical parts (4, 18, and 12) is 2.

Considering the variable k, it appears in both 4k and 18k⁴. The lowest power of k is k¹. The term k does not appear in 12, so it won’t contribute to the GCF.

Finally, we multiply our findings:

GCF = 2.

This means the greatest common factor of 4k, 18k⁴, and 12 is 2.