What is the sum of all factors of 45000 which are divisible by 10

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- June 24th 2009, 09:03 AMjashansinghalsum of factors
What is the sum of all factors of 45000 which are divisible by 10

- June 24th 2009, 10:38 AMTheAbstractionist
That would be 10 times the sum of all the factors of 4500. The sum-of-factors function has the following property: if where the are distinct primes, then

Thus So the answer to the problem is 141960. - June 25th 2009, 02:30 AMjashansinghal
can u give an easy method

- June 25th 2009, 07:23 AMTheAbstractionist
I don’t see anything wrong with the proof, particularly the formula

Shall we prove this formula? Then perhaps you’ll feel less afraid of using it. (Wink)

First, we prove that if then Note that a divisor of can be written as where and and Hence

Next, not that if is a prime and a positive integer,

Combining the two results established above gives the required formula for the sum-of-factors function (Cool)