Question

Find the greatest common factor (GCF/HCF) of the following polynomial ${a^2}{b^3}$ and ${a^3}{b^2}$.

Answer 1

Hint – In this particular question use the concept that first of all calculate all the prime factors of the given number for example the prime factors of 10 are (1, 2 and 5), prime factors are those which is divide by 1 or itself, and HCF of the two or more numbers is the multiplication of the common factors, so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given polynomials are ${a^2}{b^3}$ and ${a^3}{b^2}$.
As we know that the greatest common factor (G.C.F) or the highest common factor (H.C.F) is calculated by multiplying all the common factors of the given numbers.
So we have to first factories the polynomials and then take the common factors then multiplying these common factors together this factor is called the greatest common factor or the highest common factor (GCF/HCF) of the given polynomials.
Therefore, first calculate the factors of the first polynomial i.e. ${a^2}{b^3}$ So, the factors of ${a^2}{b^3}$ are,
${a^2}{b^3} = a \times a \times b \times b \times b$
Now calculate the factors of the second polynomial i.e. ${a^3}{b^2}$So, the factors of ${a^3}{b^2}$are
${a^3}{b^2} = a \times a \times a \times b \times b$
Now as we see that the common factors of the given polynomial are a, a, b and b
Now multiply these common factors together to get the greatest common factor or the highest common factor.
So the required greatest common factor or the highest common factor (GCF/HCF) is $a \times a \times b \times b = {a^2}{b^2}$
So the required GCF/HCF is ${a^2}{b^2}$.
So this is the required answer.

Note – Whenever we face such types of questions always remember that the GCF is greatest common factor and the HCF is highest common factor and both are same so first find out all the factors of the given polynomial then find out the common factors and multiply them which is the required (GCF/HCF) of the given polynomial.