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Question

Find the total number of proper factors of the number 35700. Also find sum of all these factors

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Solution

35700=52×22×31×71×171
The total number of factors is equal to the total number of selections from (5,5), (2,2), (3), (7), and (17), which is given by 3×3×2×2×2=72.
These include 1 and 35700. Therefore, the number of proper divisors (excluding 1 and 35700) is 722=0=70
Sum of all these factors (proper) is
(50+51+52)(20+21+22)(30+31)(70+71)(170+171)135700
=31×7×4×8×18135700=89291

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