The Pythagoreans were fascinated by perfect, abundant, deficient and amicable numbers. A counting number is said to be perfect if it is equal to the sum of its proper factors. ( " Proper" simply means not including the original number being factored). Show that 8128 is a perfect number.
2006-12-19 13:36:59 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
here are the factors of 8128:
1
2
4
8
16
32
64
4064
2032
1016
508
254
127
And they add up to 8128!
here is a link with a nice write-up on perfect numbers:
http://mathworld.wolfram.com/PerfectNumber.html
2006-12-19 13:45:15 · answer #1 · answered by firefly 6 · 1⤊ 0⤋
8128 = 1 + 4064 + 2 + 2032 + 4 + 1016 + 8 + 508 + 16 + 254 + 32 + 127 + 2
2006-12-19 21:49:44 · answer #2 · answered by _Bogie_ 4 · 0⤊ 0⤋
Start by finding the greatest integer less than the square root of 8128, which is 90.
Then, starting with 1 and moving up integer by integer up to 90, find each corresponding factor greater than 90, if one exists.
If a number is not a factor of 8128, then skip any of its multiples, as they cannot be factors either, e.g. 5 isn't a factor, so don't bother checking 10, 15, 20, etc.
Once all factors are found in this manner, add them up.
2006-12-19 21:47:37 · answer #3 · answered by Robbie 2 · 0⤊ 1⤋
Write out all the numbers that divide into 8128, like 1, 2, 4, etc. Stop at 4064, (4064*2 = 8128) See if they do really add up to 8128.
2006-12-19 21:42:15 · answer #4 · answered by J G 4 · 1⤊ 1⤋
The factors of 8128 are 1,2,2,2,2,2,2,127. These numbers do not sum to 8128.Therefore 8128 is not a perfect number.
2006-12-19 21:47:28 · answer #5 · answered by ironduke8159 7 · 0⤊ 3⤋
the factors of 8128 are
1,2,4,8,16,32,64,127,254
,508,1016,2032,4064
which when added give 8128
2006-12-19 21:46:23 · answer #6 · answered by raj 7 · 1⤊ 0⤋