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Find the sum of all positive integers $r$ that satisfy $\text{lcm}[r,700] = 700.$

 Aug 13, 2023
 #1
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All positive integers r and their sum are as follows:

 

1 , 2 , 4 , 5 , 7 , 10 , 14 , 20 , 25 , 28 , 35 , 50 , 70 , 100 , 140 , 175 , 350 , 700>>Total number=18> Total Sum= 1736

 Aug 13, 2023
 #2
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Such integers are simply the factors of \(700\). Note that \(700=2^2\cdot5^2\cdot7\), so the sum of its factors is \((1+2+4)(1+5+25)(1+7)=1736\). 

 Aug 13, 2023

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