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. Multiplying 3-Digit Number by 1-Digit Number | Three-Digit Multiplicat

    Oct 22, 24 03:26 PM

    Multiplying 3-Digit Number by 1-Digit Number
    Here we will learn multiplying 3-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. 1. Multiply 201 by 3 Step I: Arrange the numb…

    Read More

  2. Word Problems on Multiplication |Multiplication Word Problem Worksheet

    Oct 22, 24 01:23 AM

    Multiplication Word Problem
    Word problems on multiplication for fourth grade students are solved here step by step. Problem Sums Involving Multiplication: 1. 24 folders each has 56 sheets of paper inside them. How many sheets of…

    Read More

  3. Worksheet on Word Problems on Multiplication | Multiplication Problems

    Oct 22, 24 12:31 AM

    In worksheet on word problems on multiplication, all grade students can practice the questions on word problems involving multiplication. This exercise sheet on word problems on multiplication

    Read More

  4. Multiplying 2-Digit Number by 1-Digit Number | Multiply Two-Digit Numb

    Oct 21, 24 03:38 PM

    Multiplying 2-Digit Number by 1-Digit Number
    Here we will learn multiplying 2-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. Examples of multiplying 2-digit number by

    Read More

  5. Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table

    Oct 21, 24 02:26 AM

    Multiplication Table of Four
    Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times

    Read More