What is the greatest common factor of 12x and 16 y?

Answer 1

The greatest common factor of 12x and 16y is 4.

The prime factorization of the first one is: 2 . 2 . 3 . x

The prime factorization of the second one is: 2 . 2 . 2 . y

You can take 2 . 2 out of each of these.

Note: x and y are variables and have not been assigned a value. Yes, they could be 12, but that does not mean they can be broken down to 2 x 2 x 3 because they can also be 13 which can't be broken down to anything. Since these are not equations, they are nothing but x and y which are treated as prime. They become composite when you assign an exponent to them such as y2 which can be broken down to y . y

_____________________________________________________________________________________

-- If 'x' and 'y' are both integers, then the greatest common factor could be

any integer greater than 3 .

-- If 'x' and 'y' are not both integers, then there may not be any common factors at all.

-- If 'x' and 'y' are both less than ' 1 ', then the greatest common factor could be

any integer less than 4 .

-- That's why these "greatest common factor" exercises always refer only to integers,

not to algebraic expressions.

* * * * *

The answer above the line is OK, but not so the points below the line.

The concept of greatest common factor (GCF) can and is applied to algebraic expressions (point 4).

In terms of numbers, it does apply only to integers. It is meaningless for fractions because any number can divide into fractions (point 2).

The GCF of 4 and 6 is 2 (point 1).

Not sure what point 3 means.

Answer 2

c