Amicable Numbers

The FACTORS of a number are numbers which divide into it exactly (without leaving a remainder). PROPER FACTORS are all of the factors of a number except itself.

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Example

Factors of 36 are:
1, 2, 3, 4, 6, 9, 12, 18, 36

Proper factors of 36 are:
1, 2, 3, 4, 6, 9, 12, 18

Two numbers are AMICABLE if all of the proper factors of the first number add up to the second number and all of the proper factors of the second number add up to the first number.

Example

220 and 284 are an AMICABLE PAIR.

Proper factors 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

Proper factors of 284 are:
1, 2, 4, 71, 142

1 + 2 + 4 + 71 + 142 = 220

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Exercise

Which of these pairs of numbers are AMICABLE?

  1. 1184 and 1210

  2. 1450 and 1600

  3. 2620 and 2924

  4. 3600 and 4000

  5. 5020 and 5564