- Trending Categories
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Find the greatest common factor of the terms in the expression $3a^2b^2+4b^2c^2+12a^2b^2c^2$.
Given:
The given expression is $3a^2b^2+4b^2c^2+12a^2b^2c^2$.
To do:
We have to find the greatest common factor of the terms in the given expression.
Solution:
GCF:
A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.
The terms in the given expression are $3a^2b^2, 4b^2c^2$ and $12a^2b^2c^2$.
The numerical coefficient of $3a^2b^2$ is $3$
The numerical coefficient of $4b^2c^2$ is $4$
The numerical coefficient of $12a^2b^2c^2$ is $12$
This implies,
$3=3\times1$
$4=2\times2$
$12=2\times2\times3$
GCF of $3, 4$ and $12$ is $1$
The common variable in the given terms is $b$
The power of $b$ in $3a^2b^2$ is $2$
The power of $b$ in $4b^2c^2$ is $2$
The power of $b$ in $12a^2b^2c^2$ is $2$
The monomial of common literals with the smallest power is $b^2$
Therefore,
The greatest common factor of the three terms in the given expression is $b^2$.
94 Views
