Algebra and General Mathematics: Factors

Review notes in Factors topic in Algebra and General Mathematics. This will help you prepare in taking the Engineering Board Exam or simply reviewing for your Algebra subject.

Algebra and General Mathematics: Factors

FACTORS

A factor is a number or expression which divides exactly another number or expression.

Example:

2 and 4 are factors of 8

(x + y) and (x – y) are factors of (x2 – y2)

Note: the Proper Factors of a number are its entire factor except the number itself.

Example:

Factors of 24, F(24) = { 1, 2, 3, 4, 6, 8, 12, 24 }

Proper Factors, Fp = { 1, 2, 3, 4, 6, 8, 12 }

COMMON FACTORS

Common Factors are factors shared or common to the two or more numbers.

Example:

What are the common factors of 12 and 24?

Solution:

Factors of 12:

F(12) = { 1, 2, 3, 4, 6, 12 }

Factors of 24:

F(24) = { 1, 2, 3, 4, 6, 8, 12, 24 }

Therefore, the common factors of 12 and 24 are:

F(12) ⋂ F(24)  = { 1, 2, 3, 4, 6 }

LOWEST COMMON FACTORS (LCF)

The Lowes Common Factor (LCF) of two or more numbers is the common factor of all those numbers which has the lowest value.

Example: ECE Board April 1998

What is the lowest common factor of 10 and 32?

Solution:

Prime factors of 10 = 5 x 2

Prime factors of 32 = 2 x 2 x 2 x 2 x 2

F2⋂32  = 2

HIGHEST COMMON FACTORS (HCF)

The Highest Common Factor (HCF) of two or more whole numbers is the largest whole number which is a factor of both.

Example:

Find the HCF of 240, 600, and 720.

Solution:

-get all the prime factors of the numbers in canonical form

F(240)  = 3 x 5 x 24

F(600)  = 3 x 52 x 23

F(720)  = 32 x 5 x 24

Therefore, the HCF is:

HCF = 3 x 5 x 23 = 120


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