123ArticleOnline Logo
Welcome to 123ArticleOnline.com!
ALL >> Education >> View Article

Perfect Numbers I

Profile Picture
By Author: math qa22
Total Articles: 69
Comment this article
Facebook ShareTwitter ShareGoogle+ ShareTwitter Share

A factor of a number is an exact divisor of that number. Now in other words we can say , a factor of a number is the number which completely divides the given number without any remainder. Let us take some examples to understand factors.

Let us factor a number 12, factor of 12 are 1,2,3,4,6 and 12. However, none of the numbers 5,7,8,9,10 and 11 is a factor of 12.Now what are Perfect numbers? if the sum of all the factors of a number is two times the number, then the number is called Perfect number. The factors of 6 are 1,2,3 and 6.Also, 1+2+3+6=12=2*6 i.e sum of all factors of 6 = 2*6 so, 6 is a perfect number. Now let us see if 28 is the perfect number .The factors of 28 are 1,2,4,7,14 and 28.Sum of all factors of 28 = 1+2+4+7+14+28=56+2*28 So,28 is also a perfect number. Note that 12 is not a perfect number.

Procedure for finding factors
Step 1 Obtain the number whose factors are to be listed.
Step2 Divide the number by 2.If the number is divisible by 2, find the quotient and list 2 and other factor (quotient) just below 2.
Step3 Divide the number by 3.If the number is divisible ...
... by 3, find the quotient and list 3 and the quotient just below 3.
Step4 Divide the number by 4.If the number is divisible by 4, find the quotient and list 4 and the quotient just below 4
Continue this process with 5,6,7 etc. till you get a factor which has already been listed.

Let us take some example of factor, Find factors of a numbers 24:-
(a) 24 The given number is 24. Clearly, 1 and 24 are its factors. So, we list 1 and 24.We find that if we divide 24 by 2, the quotient is 12 and the remainder is zero. Therefore, 24 is divisible by 2. S, we list 2 and 12.When 24 is divided by 3, the quotient is 8 and the remainder is zero.
So,24 is divisible by 3 and we list 3 and 8.Now, we divide 24 by 4. Clearly, when we divide 24 by 4, we obtain 6 as the quotient and the remainder as zero. So, 24 is also divisible by 4 and we list 4 and 6.Clearly,24 is not divisible by 5. The next number is 6, which has already been listed as a factor.

So, we stop the procedure and list the
factors of 24 as given below:
1 2 3 4
24 12 8 6
(b) The given number is 64.To factor a number clearly; it is divisible by 1,2,4,8 etc. So, its factors or Factor Numbers are as listed below.1 2 4 8 64 32 16 8
(c) The given number is 144. Clearly ,it is divisible by 1,2,4,6,8,12,16,24,etc.So,factors of 144 are:1 2 3 4 6 8 9 12 144 72 48 36 24 18 16 12

Know more about the Exponential Function Definition, online tutoring,Properties Of Exponential Functions. Online tutoring will help us to learn and do our homework very easily without going here and there.

Total Views: 157Word Count: 530See All articles From Author

Add Comment

Education Articles

1. Guaranteed Grades: Pay Someone To Take My Exam
Author: Doug Macejkovic

2. Blocks Before Books
Author: Michale

3. Azure Devops Training Online | Azure Devops Online Training
Author: visualpath

4. Learn Python Programming - from Basics To advanced
Author: vishal more

5. Data Engineering Course In Hyderabad | Aws Data Analytics Training
Author: naveen

6. Oci Online Training | Oracle Cloud Infrastructure In Hyderabad
Author: visualpath

7. Best Salesforce Data Cloud Certification Training
Author: visualpath

8. The Benefits Of Online Dry Needling Certification
Author: Daulat

9. Top Google Cloud Data Engineer Training In Bangalore
Author: Visualpath

10. Aima’s Management Diploma: The Smart Choice For Future Leaders
Author: Aima Courses

11. How Regular Mock Test For Bank Help You Crack Bank Exams
Author: Ayush Sharma

12. Debunking The Myth: Is Preschool Just Playtime?⁠
Author: Kookaburra

13. Cps Global School: A World-class Learning Destination In Chennai
Author: CPS Global School

14. Chennai Public School: Shaping Future Leaders Through Excellence In Education
Author: Chennai Public School

15. "transform Your Data Analysis With Lcc Computer Education's Excel Training"
Author: Khushi Gill

Login To Account
Login Email:
Password:
Forgot Password?
New User?
Sign Up Newsletter
Email Address: