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People have been searching for number patterns since ancient times.
Mathematicians noticed that some numbers are equal to the sum of
all of their
factors (but
not including the number itself).
6 is a number that equals the sum of its factors: 1 + 2 + 3 equal
6.
Numbers like 6 that equal the sum of their factors are called
perfect numbers.
6 is the first
perfect
number .
4 is not a
perfect number
because the sum of its factors (besides 4 itself), 1+2, is less
than 4. Numbers like 4 are known as
deficient numbers . What does the word
deficient mean? Why do you think numbers having factors adding to
less than the number itself are called deficient numbers?
12 is not a
perfect number
because the sum of its factors, 1+2+3+4+6 is greater than 12.
Numbers like 12 are known as
abundant numbers . What does the word
abundant mean? Why do you think numbers having factors adding to
more than the number itself are called abundant numbers?
Since the time of Pythagoras (about 500 BC), mathematicians have
tried to find as many perfect numbers as they can. By 1999 only 38
perfect numbers had been found.
Can you find the next perfect
number after 6?
Could a perfect number also be a
prime number?
Do you think there are more
perfect, deficient or abundant numbers?
Add the factors of all the numbers
up to 50. Was your guess correct?
Can you find any patterns in your
results?