- Before you begin, it might help to remember that the divisors
of
a number are its whole number factors. In other words, the divisors are
the numbers that "divide evenly" into the given number and leave no
remainder.
- So for example, the divisors of 10 are the numbers 1, 2, 5 and 10. No
other numbers divide evenly into 10.
- Also, the proper divisors of a number are the divisors that
are
less than the number.
- So the proper divisors of 10 are 1, 2 and 5.
- Before you try solving the problem about 1184, you should explain
why
284 and 220 are amicable by listing all the divisors of 284 and showing
that
they add up to 220, and then listing all the divisors of 220 and showing
that
they add up to 284.
- For a special challenge, can you find another pair of amicable
numbers,
besides 220 and 284, and 1184 and its mate? You'll have to look at some
big
numbers!
As always, be sure to explain the
work you did to arrive
at your answers!
Pythagoras (the right triangle guy)
discovered amicable or "friendly" numbers. Two positive
integers are amicable if each is the sum of the proper divisors of the
other. 284 is amicable with 220. What number is amicable to 1184?