Let us make a review on finding gcf of any two numbers before we start learning how to find gcf of monomials.
Introduction to GCF of monomials:
Greatest common factor is abbreviated as GCF. To find gcf of any two numbers, we have to write the prime factors of the numbers and pick out the common terms and find the product.
Ex 1: Consider 4 and 8.
Prime factors of 4 = 2 x 2
Prime factors of 8 = 2 x 2 x 2
Common factors are 2 and 2
The product of common factors are 2 x 2 = 4
GCF of 4 and 8 is 4
Monomial is an mathematical expression that has only one term consisting of constants and variables raised to any exponents connected by mathematical operation multiplication or division.
Ex: 3x, 2xyz, 6x2y3z4
How to Find the Gcf of Given Monomials:
Consider any two monomials, say 3a3, 9a5
Step 1: Write the factors of the two monomials.
3a3 = 3 x a x a x a
9a5 = 3 x 3 x a x a x a x a x a
Step 2: Pick out the common factors
Common factors are 3, a, a, a
Step 3: Find their product
Product is 3a3
Step 4: Write the product as gcf
GCF of the given monomials is 3a3
By regular practice, one could say the gcf of monomial by seeing the monomials.
Consider x2, x3
The term with lowest power is the gcf
So, x2 is the gcf
Consider a2bc, ab2c, abc2
There are three monomials. Each monomial has the same variables a, b, c
Pick up the variables that has least power in the given monomials
It is a, b and c
So, GCF is abc.
With the above ideas, let us do some problems on GCF .Having problem with what is standard form keep reading my upcoming posts, i will try to help you.
Problems to Find the Gcf of a Monomial:
Ex 1: Find gcf of p8, p9, p7
Sol:
Step 1: Check whether all the terms has same variables
Step 2: Pick out the term has that least power.
It is p7
Step 3: Write the solution.
gcf is p7
Ex 2: Find gcf of the monomials 14m2n, 28mn2, 21m3n3
Sol:
Step 1: Find the gcf of the three numbers.
14 = 2 x 7
28 = 4 x 7
21 = 3 x 7
Greatest common factor is 7
Step 2: The monomials has the same variables m and n.
Step 3: Pick out the variables that hs least power
It is m and n
Step 4: Gcf is 7mn
Introduction to GCF of monomials:
Greatest common factor is abbreviated as GCF. To find gcf of any two numbers, we have to write the prime factors of the numbers and pick out the common terms and find the product.
Ex 1: Consider 4 and 8.
Prime factors of 4 = 2 x 2
Prime factors of 8 = 2 x 2 x 2
Common factors are 2 and 2
The product of common factors are 2 x 2 = 4
GCF of 4 and 8 is 4
Monomial is an mathematical expression that has only one term consisting of constants and variables raised to any exponents connected by mathematical operation multiplication or division.
Ex: 3x, 2xyz, 6x2y3z4
How to Find the Gcf of Given Monomials:
Consider any two monomials, say 3a3, 9a5
Step 1: Write the factors of the two monomials.
3a3 = 3 x a x a x a
9a5 = 3 x 3 x a x a x a x a x a
Step 2: Pick out the common factors
Common factors are 3, a, a, a
Step 3: Find their product
Product is 3a3
Step 4: Write the product as gcf
GCF of the given monomials is 3a3
By regular practice, one could say the gcf of monomial by seeing the monomials.
Consider x2, x3
The term with lowest power is the gcf
So, x2 is the gcf
Consider a2bc, ab2c, abc2
There are three monomials. Each monomial has the same variables a, b, c
Pick up the variables that has least power in the given monomials
It is a, b and c
So, GCF is abc.
With the above ideas, let us do some problems on GCF .Having problem with what is standard form keep reading my upcoming posts, i will try to help you.
Problems to Find the Gcf of a Monomial:
Ex 1: Find gcf of p8, p9, p7
Sol:
Step 1: Check whether all the terms has same variables
Step 2: Pick out the term has that least power.
It is p7
Step 3: Write the solution.
gcf is p7
Ex 2: Find gcf of the monomials 14m2n, 28mn2, 21m3n3
Sol:
Step 1: Find the gcf of the three numbers.
14 = 2 x 7
28 = 4 x 7
21 = 3 x 7
Greatest common factor is 7
Step 2: The monomials has the same variables m and n.
Step 3: Pick out the variables that hs least power
It is m and n
Step 4: Gcf is 7mn
