Two numbers are said to be amicable if each number is the sum of the proper divisors of the other.
A proper divisor of a number is any divisor of the number except the number itself.
For example, the proper divisor of 12 are 1, 2, 3, 4, and 6.
Notice that 12 is not included in the list although it is a divisor of 12.
Now we will show that 220 and 284 are amicable numbers.
The proper divisors of 284 are 1, 2, 4, 71, and 142
1 + 2 + 4 + 71 + 142 = 220
The sum of the proper divisors of 284 is equal to 220
The proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110
1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284
The sum of the proper divisors of 220 is equal to 284.
Therefore, we can conclude that 220 and 284 are amicable numbers.
A short list of amicable numbers are shown below
220 284
1184 1210
2620 2924
5020 5564
6232 6368
10744 10856
12285 14595
......
.......
437456 455344
469028 486178
503056 514736
522405 525915
600392 669688
609928 686072
Let us show that 600392 and 669688 are amicable
Use this calculator to quickly see the factors. That way you don't have to waste time.
The proper factors of 609928 are 1, 2, 4, 8, 11, 22, 29, 44, 58, 88, 116, 232, 239, 319, 478, 638, 956, 1276, 1912, 2552, 2629, 5258, 6931, 10516, 13862, 21032, 27724, 55448, 76241, 152482, and 304964
Add all the numbers and it will equal to 686072
The proper factors of 686072 are 1, 2, 4, 8, 191, 382, 449, 764, 898, 1528, 1796, 3592, 85759, 171518, and 343036
Add all the numbers above and you will get 600392
600392 and 669688 are indeed amicable
Dec 14, 18 04:05 PM
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