What is the greatest common factor of 18a4b3

Question

and 21a8b3
?

Answer 1

To find the greatest common factor (GCF) of $18a^4{b}^3$ and $21a^8{b}^3$, we start by determining the GCF of the numerical coefficients and then the GCF of each variable part.

1. Numerical Coefficients:

   • The coefficients are 18 and 21.
   • The prime factorization of 18 is: $$18=2\times 3^2$$
   • The prime factorization of 21 is: $$21=3\times 7$$
   • The common factor from the prime factorizations is $3$.

2. Variable Part:

   • For $a^4$ and $a^8$, the GCF is the variable raised to the lowest exponent: $$\text{GCF}(a^4,a^8)=a^{min(4,8)}=a^4$$
   • For $b^3$ in both terms, since they are the same, the GCF is: $$\text{GCF}(b^3,b^3)=b^3$$

3. Combine the GCFs:

   • Combining all these, we get: $$\text{GCF}(18a^4{b}^3,21a^8{b}^3)=3\cdot a^4\cdot b^3$$

Thus, the greatest common factor of $18a^4{b}^3$ and $21a^8{b}^3$ is: $$\boxed{{\displaystyle 3a^4{b}^3}}$$