Divsiors
There exists a positive integer satisfying the property that its largest proper divisor is equal to 15 times its second smallest positive divisor.
If the total possible values of is , and the smallest possible value of is , submit your answer as .
Bonus: Solve this question again, but this time, replace the number 15 with the number 17 instead.
The answer is 62.
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1 solution
let the smallest possible divisor be k (where k >1)
=> k n is its greatest divisor
=> n = 1 5 × k 2
=> 3 and 5 have to be the factors of n
so for k to be smallest divisor k <=3
giving us 2 possible values of n only, that are for k=2 and k=3;
=> p =2;
=> n = 60,135;
=> q = 60;
=> p+q = 62 ;