Factors of Algebraic Expressions is the product of numbers, algebraic expressions, algebraic variables, etc. Here the numbers, algebraic expressions, algebraic variables are the factors of the algebraic expressions. Generally, factors of a number can be calculated with the product of its multiples. You can learn more about **Factorization** and related concepts by always seeking help from us. For example, by multiplying 2, 3, 7, we get 42. Therefore, 2, 3, 7 are the factors of 42. Factors of a given number are the product of two or more numbers.

## Basics of Algebra Expressions

**Expressions:** Expressions are formed with constants and variables. 2x – 5 is an expression that formed with the variable x and numbers 2 and 5.

**Terms, factors, and Coefficients:** Algebraic expression is the combination of terms, coefficients, and factors. For example, in 5x + 7, 5x and 7 are terms, x and 7 are factors, and 5 and 7 are numeric coefficients.

**Monomials, binomials, and Polynomials:** An expression having only one term is known as a monomial, an expression having two terms are called binomial. Also, an expression with various terms and with a non-zero coefficient is called as Polynomials.

### Factors of the Monomials

Product of variable and numbers can form a monomial that consists of different factors.

1. Write all the possible factors of 5ab^{2}?

Solution:

The possible factors of 5 are 1 and 5.

The possible factors of ab² are a, b, b², ab, ab²

All possible factors of 5ab² are a, b, b^{2}, ab, ab^{2}, 1, 5, 5a, 5b, 5b^{2}, 5ab, and 5ab^{2}.

2. Write down all the factors of 7m^{2}n?

Solution:

The possible factors of 7 are 1 and 7.

The possible factors of m^{2}n are m, n, mn, m^{2}, m^{2}n.

All possible factors of 7m^{2}n are m, n, mn, m^{2}, m^{2}n, 1, 7, 7m, 7n, 7mn, 7m^{2}, 7m^{2}n.

3. Write all the factors of 3x²y²?

Solution:

The possible factors of 3 are 1 and 3.

The possible factors of x²y² are x, y, xy, x², y², x²y, xy², x²y²

All possible factors of 3x²y² are x, y, xy, x², y², x²y, xy², x²y², 1, 3, 3x, 3y, 3xy, 3x², 3y², 3x²y, 3xy², 3x²y²

4. Write down all the factors of 3xyz?

Solution:

The possible factors of 3 are 1 and 3.

The possible factors of xyz are x, y, z, xy, xz, yz, xyz

All possible factors of 3xyz are x, y, z, xy, xz, yz, xyz, 1, 3, 3x, 3y, 3z, 3xy, 3xz, 3yz, 3xyz

### Highest Common Factor (HCF) of Monomials

The H.C.F. of two or more monomials is the product of the H.C.F. of the numerical coefficients and the common variables with the least powers.

1. Find the H.C.F. of 12a^{3}b^{2}, 14a^{2}b^{3}, 6ab^{4}.

Solution:

Firstly, find the HCF of given terms.

HCF of their numerical coefficients 12, 14, and 6 is 2.

HCF of literal coefficients:

The lowest power of a is 1.

The lowest power of b is 2.

Therefore, the HCF of literal coefficients is ab^{2}.

HCF of two or more monomials = (HCF of their numerical coefficients) × (HCF of their literal coefficients)

HCF of 12a^{3}b^{2}, 14a^{2}b^{3}, 6ab^{4} is 2ab^{2}.

The final answer is 2ab^{2}.

2. Find the H.C.F. of 6xy, 18x^{2}y?

Solution:

Firstly, find the HCF of given terms.

HCF of their numerical coefficients 6 and 18 is 6.

HCF of literal coefficients:

The lowest power of x is 1.

The lowest power of y is 1.

Therefore, the HCF of literal coefficients is xy.

HCF of two or more monomials = (HCF of their numerical coefficients) × (HCF of their literal coefficients)

HCF of 6xy, 18x^{2}y is 6xy.

The final answer is 6xy.

3. Find the H.C.F. of 9abc² and 36ac?

Solution:

Firstly, find the HCF of given terms.

HCF of their numerical coefficients 9 and 36 is 9.

HCF of literal coefficients:

The lowest power of a is 1.

The lowest power of b is 0.

The lowest power of c is 1.

Therefore, the HCF of literal coefficients is ac.

HCF of two or more monomials = (HCF of their numerical coefficients) × (HCF of their literal coefficients)

HCF of 9abc² and 36ac is 9ac.

The final answer is 9ac.