Algebra and General Mathematics: Factors

(Last Updated On: December 8, 2017)

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

Algebra and General Mathematics: Factors
Rate this:

Add Comment

© 2017 PinoyBIX Engineering. © 2017 All Rights Reserved | Donate
Basic Television - Grob TV  Chapter Exercises
Basic Television – Grob TV Chapter Exercises
Series of Multiple Choice Questions in Engineering Mathematics
Series of Multiple Choice Questions in Engineering Mathematics
Complete Practice Quiz in Electronic Devices and Circuit Theory
Complete Practice Quiz in Electronic Devices and Circuit Theory
Complete Practice Quiz in Data Communications and Networking
Complete Practice Quiz in Data Communications and Networking
Online Tool: Color Code Conversions
Online Tool: Color Code Conversions
Online Tool: Weight Measurement Conversions
Online Tool: Weight Measurement Conversions
Online Tool: Temperature Measurement Conversions
Online Tool: Temperature Measurement Conversions
Online Tool: Length Measurement Conversions
Online Tool: Length Measurement Conversions

Get FREE Review Course
in your inbox

Subscribe to our mailing list and get reviewers and updates to your email inbox.

Thank you for subscribing.

Something went wrong.