Enter two numbers to check if they are amicable.
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.
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.
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.
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.