Perfect
Number
Let us consider the number 6, what are
the numbers (positive integers) that can fully divide 6 without
leaving any remainder ? Those numbers are : 1 , 2, 3 and 6. These are
called factors of 6. Obviously 1 is a factor of every number, and
every number is a factor of itself. Among the factors of 6 the
numbers 1,2, and 3 are called Proper Factors of 6. So when we
say proper factor of 6, we mean a factor of 6 other than 6 itself.
Now if we take all the proper factors
of 6 and add them, what do we get ?
1+2+3=6
Thus we see that the sum of all the
proper factors of 6 is equal to 6.
Also consider the number 28. Let us
make a list of all its divisors ( factors). These are : 1,2,4,7,14
and 28.
And we see 1+2+4+7+14=28
Thus the sum of all the proper factors
of 28 is 28
Numbers like 6 and 28 are called
Perfect Numbers. A number that is equal to the sum of all its proper
factors is called Perfect Number.
Next two perfect numbers are 496 and
8128.
