Skip to content

Latest commit

 

History

History

Amicable Number

Folders and files

NameName
Last commit message
Last commit date

parent directory

..
Amicable_Number.java
Amicable_Number.java
 
 
README.md
README.md
 
 

README.md

Amicable Number

The amicable numbers are two different numbers (a pair of numbers) so related that the sum of the proper divisors (excluding the number itself) of one of the numbers is equal to the other. A proper divisor of a number is a divisor other than the number itself. It is also known as friendly numbers.

Simply

The sum of the divisor of the first number = The sum of the divisor of the second number

The sum of the divisor of the second number = The sum of the divisor of the first number

The smallest pair of amicable numbers is (220, 284).

Because :

  1. The divisor of 220 are: 1,2,4,5,10,11,20,22,44,55,and 110

  2. The sum of divisor of 220 is = 284**

  3. The divisor of 284 are: 1,2,4,71,142

  4. The sum of divisor of 284 is = 220

We observe that the sum of the divisors of the first number is equal to the second number, and the sum of divisor of the second number is equal to the first number. Hence, the given pair (220, 284) is an amicable pair.

Amicable Numbers Example

Pair of Numbers Divisors of the First Number Sum of Divisors of the First Number Divisors of the Second Number Sum of Divisors of the Second Number Amicable/ Not Amicable
220, 284 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 284 1, 2, 4, 71, 142 220 Amicable
1184, 1210 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592 1210 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605 1184 Amicable
2620, 2924 1, 2, 4, 5, 10, 20, 131, 262, 524, 655, 1310 2924 1, 2, 4, 17, 34, 43, 68, 86, 172, 731, 1462 2620 Amicable
5020, 5564 1, 2, 4, 5, 10, 20, 251, 502, 1004, 1255, 2510 5564 1, 2, 4, 13, 26, 52, 107, 214, 428, 1391, 2782 5020 Amicable
6232, 6368 1, 2, 4, 8, 19, 38, 41, 76, 82, 152, 164, 328, 779, 1558, 3116 6368 1, 2, 4, 8, 16, 32, 199, 398, 796, 1592, 3184 6232 Amicable

Some other amicable pair numbers are (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084), and (66928, 66992).

Steps to Find Amicable Number

  1. Read or initialize two numbers (N1, N2) from the user.
  2. Find the divisor (divOfN1, divOfN2) of both numbers.
  3. Find the sum of divisors (sumdiv1, sumdiv2) of both numbers.
  4. Check if the sum of divisors of one number is equal to the other number or not.
    • If equal, the pair of numbers is amicable.
    • Else, not amicable.