Common Monomial Factor

Monomial means a single term of a polynomial. Ex : 2xy or 8mn or 3x2. Monomial factor is a factor which has a variable and a term with some exponents. Common monomial factor means finding the common factor from the given set of monomials.  The common monomial factor can be a combination of number and variable, a variable, a number, two or more numbers and two or more variables.

Steps to find the common monomial factor:

Step 1: write down all the given monomials.

Step 2: write the factors for each given monomial separately.

Step 3: Highlight the common factor from all the factors.

Step 4: The common factors are the common monomial factor.

Example based on Common monomial factor:

Ex 1: Find the common monomial factor for the monomials 9pq and 12pq.

Sol:

The given monomials are 9pq and 12pq

The factors of 9pq are 3, 3, p and q

The factors of 12pq are 2, 2, 3, p and q.

The common factors are 3, p and q.

The common monomial factor is 3pq.

Ex 2: Find the common monomial factor for the monomials 9x3y2 and 15xyz.

Sol:

The given monomials are 9x3y2 and 15xyz.

The factors of the monomial 9x3y2 is 3, 3, x, x, x, y and y and the factors 15xyz is 3, 5, x, y and z

The common factors are 3, x and y.

The common monomial factor is 3, x and y. It can be written as 3*x*y=> 3xy.

Ex 3:Find the common monomial factor for the monomials 25a2bc, 252a2b and 20 a2b2.

Sol:

The given monomials are 25a2bc, 252a2b and 20 ab2.

The factors of 25a2bc is 5, 5, a, a, b and c.

The factors of 252a2b is 5, 5, 5, 5, a, a and b

The factors of 20 a2b2  is 2, 2, 5, a, a, b and b.

The common factors are 5, a, a and b.

The common monomial factor is 5a^2b.



Ex 4:Find the common monomial factor for x, yz and xyz.

Sol:

The given monomials are x, yz and xyz.

The factors of x is x.

The factors of yz are y and z.

The factors of xyz are x, y and z.

The common monomial factor is 0 because there is no common factor from the given monomials.