Amicable Numbers Checker

Enter two numbers to check if they are amicable.

Amicable Numbers Check

Result

What Are Amicable Numbers?

Amicable numbers are a pair of distinct positive integers where the sum of the proper divisors (excluding the number itself) of each number equals the other number. For example: 220 and 284 are amicable numbers because: The sum of the divisors of 220 is 284 and the sum of the divisors of 284 is 220.

How to Determine if Two Numbers Are Amicable

  • Find the Divisors: Calculate all proper divisors for both numbers (excluding the numbers themselves).
  • Sum the Divisors: Add up the divisors for each number.
  • Check the Result: If the sum of the divisors of the first number equals the second number and the sum of the divisors of the second number equals the first number, they are amicable numbers. Otherwise, they are not.
  • Examples

    Example 1: Are 220 and 284 amicable numbers?

    Solution:

    1. Find the Divisors:

    Divisors of 220: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110

    Divisors of 284: 1, 2, 4, 71, 142

    2. Sum the Divisors:

    Sum of Divisors of 220: 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284

    Sum of Divisors of 284: 1 + 2 + 4 + 71 + 142 = 220

    Conclusion: 220 and 284 are amicable numbers.

    Example 2: Are 60 and 84 amicable numbers?

    Solution:

    1. Find the Divisors:

    Divisors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30

    Divisors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42

    2. Sum the Divisors:

    Sum of Divisors of 60: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 = 108

    Sum of Divisors of 84: 1 + 2 + 3 + 4 + 6 + 7 + 12 + 14 + 21 + 28 + 42 = 140

    Conclusion: 60 and 84 are not amicable numbers.

    Example 3: Are 1184 and 1210 amicable numbers?

    Solution:

    1. Find the Divisors:

    Divisors of 1184: 1, 2, 4, 8, 16, 37, 74, 148, 296, 592

    Divisors of 1210: 1, 2, 5, 10, 121, 242, 605

    2. Sum the Divisors:

    Sum of Divisors of 1184: 1 + 2 + 4 + 8 + 16 + 37 + 74 + 148 + 296 + 592 = 1210

    Sum of Divisors of 1210: 1 + 2 + 5 + 10 + 121 + 242 + 605 = 1184

    Conclusion: 1184 and 1210 are amicable numbers.