HCF of monomials

Key Notes:

Definition of Monomials:

Monomials are algebraic expressions with one term. Examples include 3x, -5y², and 4ab.

Understanding HCF (Highest Common Factor):

HCF of monomials involves finding the highest common factor of the numerical coefficients and variables’ highest powers in the monomials.

Steps to Find HCF of Monomials:

  • Step 1: Identify the numerical coefficients of the monomials.
  • Step 2: Identify the variables and their highest powers in each monomial.
  • Step 3: Determine the lowest powers of the variables common to all monomials.
  • Step 4: Multiply the HCF of numerical coefficients by the common variables raised to their lowest powers.

Example: Find the HCF of 6xy² and 15x²y³.

  • Numerical coefficients: HCF of 6 and 15 is 3.
  • Variables: HCF of x (power 1) and y (power 2) is xy².
  • HCF of monomials = 3xy².

Application in Simplification:

HCF of monomials is crucial in simplifying algebraic expressions and solving equations involving variables.

To find the highest common factor (HCF) of two or more monomials, find the prime factorisation of each monomial, identify the common factors, and multiply them together.

Learn with an example

🏚️Find the highest common factor.

9a3, 6a3

Write your answer as a constant times a product of single variables raised to exponents.——-

First, factorise each monomial and find the common factors.

9a3=3 . 3 . a . a . a

6a3=2 . 3 . a . a . a

The common factors are 3, a, a and a. Multiply them to find the highest common factor.

3 . a . a . a=3a3

The highest common factor is 3a3.

🏚️ Find the highest common factor.

6w, 2w3

Write your answer as a constant times a product of single variables raised to exponents.——-

First, factorise each monomial and find the common factors.

6w=2 . 3 . w

2w3=2 . w . w . w

The common factors are 2 and w. Multiply them to find the highest common factor.

2 . w=2w

The highest common factor is 2w.

🏚️ Find the highest common factor.

2y2, 10y

Write your answer as a constant times a product of single variables raised to exponents.——

First, factorise each monomial and find the common factors.

2y2=2 . y . y

10y=2 . 5 . y

The common factors are 2 and y. Multiply them to find the highest common factor.

2 . y=2y

The highest common factor is 2y.

let’s practice!