Answer:
3xy2
Step-by-step explanation:
GCF is the largest factors which are common in two or more numbers.
We find the GCF of two or more number number by breaking each number into their factor and then observe which factors are common in the group and then we multiple the common number to get the GCF.
Lets understand this by an example
GCF of 24 and 36
factors of 12 = 2*2*2*3 , factors of 36 = 2*2*3*3
hence we see that 2,2 and 3 are common in 12 and 36 hence
GCF will be 2*2*3 = 12
Coming back to problem
given
Expression 1 is 3xy^2
factor of 3xy^2 = 3*x*y*y
Expression 2 is 42xy4
factor of 42xy4 = 2*3*7*x*y*y*y*y
common factor between the two expressions are
3, x, y , y
hence GCF will be = 3*x*y*y =3xy2 Answer
The greatest common factor of [tex]\mathbf{3xy^2}[/tex] and [tex]\mathbf{42xy^4}[/tex] is [tex]\mathbf{3xy^2}[/tex]
The expressions are given as:
[tex]\mathbf{3xy^2}[/tex] and [tex]\mathbf{42xy^4}[/tex]
Factor both expressions
[tex]\mathbf{3xy^2= 3 \times x \times y \times y}[/tex]
[tex]\mathbf{42xy^4= 2 \times 3 \times 7 \times x \times y \times y \times y \times y}[/tex]
The common factor is calculated as:
[tex]\mathbf{Factor = 3 \times x \times y \times y}[/tex]
Multiply each term
[tex]\mathbf{Factor = 3xy^2}[/tex]
Hence, the greatest common factor of [tex]\mathbf{3xy^2}[/tex] and [tex]\mathbf{42xy^4}[/tex] is [tex]\mathbf{3xy^2}[/tex]
Read more about greatest common factors at:
https://brainly.com/question/11221202
