Write down all the possible factors for each of the following expressions. Determine the H.C.F. of the algebraic expression.

The prime factorization of $3a^2b$ is $3 \cdot a \cdot a \cdot b$.
The possible factors are combinations of these prime factors:

The prime factorization of $4ab^2$ is $2 \cdot 2 \cdot a \cdot b \cdot b$.
The possible factors are combinations of these prime factors:

of the numerical coefficients.
The numerical coefficients are 3 and 4.
Factors of 3: $1, 3$
Factors of 4: $1, 2, 4$
The H.C.F. of 3 and 4 is 1.

of the variable $a$.
The terms have $a^2$ and $a^1$. The lowest power of $a$ is $a^1$.
The H.C.F. of $a^2$ and $a$ is $a$.

of the variable $b$.
The terms have $b^1$ and $b^2$. The lowest power of $b$ is $b^1$.
The H.C.F. of $b$ and $b^2$ is $b$.

of the numerical and variable parts.
The H.C.F. of the algebraic expression $3a^2b + 4ab^2$ is the product of the H.C.F.s found in Steps 1, 2, and 3.