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.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

RSS

  1. Addition of Decimals | How to Add Decimals? | Adding Decimals|Addition

    Apr 17, 25 01:17 PM

    We will discuss here about the addition of decimals. Decimals are added in the same way as we add ordinary numbers. We arrange the digits in columns and then add as required. Let us consider some

    Read More

  2. Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

    Apr 17, 25 12:21 PM

    Expanded form of Decimal
    Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

    Read More

  3. Math Place Value | Place Value | Place Value Chart | Ones and Tens

    Apr 16, 25 03:10 PM

    0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are one-digit numbers. Numbers from 10 to 99 are two-digit numbers. Let us look at the digit 6 in the number 64. It is in the tens place of the number. 6 tens = 60 So…

    Read More

  4. Place Value and Face Value | Place and Face Value of Larger Number

    Apr 16, 25 02:55 PM

    Place Value of 3-Digit Numbers
    The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know th…

    Read More

  5. Face Value and Place Value|Difference Between Place Value & Face Value

    Apr 16, 25 02:50 PM

    Place Value and Face Value
    What is the difference between face value and place value of digits? Before we proceed to face value and place value let us recall the expanded form of a number. The face value of a digit is the digit…

    Read More