Question

Of two monomials Ion factor of 12a³ and 8c

Answer 1

The greatest common factor (GCF) of 12a³ and 8c is 4ac. To find the GCF, we compare the prime factorization of each monomial and take the highest power of each variable that appears in both monomials.

Step-by-step explanation:

To find the greatest common factor (GCF) of two monomials, we need to find the highest power of each variable that appears in both monomials and multiply them together. For the monomials 12a³ and 8c, the GCF is 4ac. Let's break it down step by step:

1. The prime factorization of 12a³ is 2² * 3 * a³.
2. The prime factorization of 8c is 2³ * c.
3. By comparing the powers of the variables, we can see that the highest power of 2 that appears in both monomials is 2², the highest power of 3 is 3⁰, and the highest power of a and c is a¹ and c¹ respectively. Multiplying all these highest powers together gives us the GCF: 2² * 3⁰ * a¹ * c¹ = 4ac.