Highest Common Factor of Monomials

How to find the highest common factor of monomials?

To find the highest common factor (H.C.F.) or greatest common factor (G.C.F.) of two or more monomials is the product of the H.C.F. of their numerical coefficients and the H.C.F. of their literal coefficients.

Note: Note: The H.C.F. of literal coefficients is each common literal with the lowest power.


Solved examples to find highest common factor of monomials:

1. Find the H.C.F. of 4x2y3 and 6xy2z.

Solution:

The H.C.F. of numerical coefficients = The H.C.F. of 4 and 6.

Since, 4 = 2 × 2 = 22 and 6 = 2 × 3 = 21 × 31

Therefore, the H.C.F. of 4 and 6 is 2


The H.C.F. of literal coefficients = The H.C.F. of x2y3 and xy2z = xy2

Since, in x2y3 and xy2z, x and y are common.

The lowest power of x is x.

The lowest power of y is y2.

Therefore, the H.C.F. of x2y3 and xy2z is xy2.

Thus, the H.C.F. of 4x2y3 and 6xy2z

= The H.C.F. of numerical coefficients × The H.C.F. of literal coefficients

= 2 × (xy2)

= 2xy2.



2. Find the H.C.F. of 8a3b2c and 12abc2.

Solution:

The H.C.F. of numerical coefficients = The H.C.F. of 8 and 12.

Since, 8 = 2 × 2 × 2 = 23 and 12 = 2 × 2 × 3 = 22 × 31

Therefore, the H.C.F. of 8 and 12 is 4

The H.C.F. of literal coefficients = The H.C.F. of a3b2c and abc2 = abc

Since, in a3b2c and abc2, a, b and c are common.

The lowest power of a is a.

The lowest power of b is b.

The lowest power of c is c.

Therefore, the H.C.F. of a3b2c and abc2 is abc.

Thus, the H.C.F. of 8a3b2c and 12abc2

= The H.C.F. of numerical coefficients × The H.C.F. of literal coefficients

= 4 × (abc)

= 4abc.






8th Grade Math Practice

From Highest Common Factor of Monomials to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

RSS

  1. Perimeter of a Square | How to Find the Perimeter of Square? |Examples

    Apr 25, 24 05:34 PM

    Perimeter of a Square
    We will discuss here how to find the perimeter of a square. Perimeter of a square is the total length (distance) of the boundary of a square. We know that all the sides of a square are equal. Perimete…

    Read More

  2. Perimeter of a Triangle | Perimeter of a Triangle Formula | Examples

    Apr 25, 24 05:13 PM

    Perimeter of a Triangle
    We will discuss here how to find the perimeter of a triangle. We know perimeter of a triangle is the total length (distance) of the boundary of a triangle. Perimeter of a triangle is the sum of length…

    Read More

  3. Perimeter of a Rectangle | How to Find the Perimeter of a Rectangle?

    Apr 25, 24 03:45 PM

    Perimeter of a Rectangle
    We will discuss here how to find the perimeter of a rectangle. We know perimeter of a rectangle is the total length (distance) of the boundary of a rectangle. ABCD is a rectangle. We know that the opp…

    Read More

  4. Dividing 3-Digit by 1-Digit Number | Long Division |Worksheet Answer

    Apr 24, 24 03:46 PM

    Dividing 3-Digit by 1-Digit Number
    Dividing 3-Digit by 1-Digit Numbers are discussed here step-by-step. How to divide 3-digit numbers by single-digit numbers? Let us follow the examples to learn to divide 3-digit number by one-digit nu…

    Read More

  5. Symmetrical Shapes | One, Two, Three, Four & Many-line Symmetry

    Apr 24, 24 03:45 PM

    Symmetrical Figures
    Symmetrical shapes are discussed here in this topic. Any object or shape which can be cut in two equal halves in such a way that both the parts are exactly the same is called symmetrical. The line whi…

    Read More