What is the greatest common factor of 45a^2b and 15ab ?
To find the greatest common factor of 45a^2b and 15ab, we need to determine the highest power of each prime factor that is common to both terms.
The prime factorization of 45a^2b is 3^2 * 5 * a^2 * b.
The prime factorization of 15ab is 3 * 5 * a * b.
To find the greatest common factor, we take the product of the lowest power of each prime factor that is common to both terms.
The lowest power of 3 that is common to both terms is 1.
The lowest power of 5 that is common to both terms is 1.
The lowest power of a that is common to both terms is 1.
The lowest power of b that is common to both terms is 1.
Therefore, the greatest common factor of 45a^2b and 15ab is 3 * 5 * a * b, which simplifies to 15ab.