The sum of the smallest two factors of an integer n is 6 and the sum of the two largest factor is 1122. Find n.
1 is a factor of every integer so the two smallest factors must be 1 and 5 which means that n is not divisable by 2 or by 3
The sum of the 2 largest factors is 1122. So the number n must be smaller than 1122/2 = 561
So one is 561-x and the other is 561+x
Maybe one is a multiple of 5 So maybe x=6t or 4t
x can't be 6t because 561 is divisable by 3 so 561*6t is also divisable by 3 which is not allowed.
What about x=4t
that would give us 561+4t and 561-4t
I cannot see any obvious reason why this can't be true.
I will try t values one at a time and see if I can find one that works
t | 1 |
565 | |
557 |
That one was easy, t =1 is a contender.
Well 565 does not have 2 or 3 as a factor and neither does 557 so they could be right.
557+565 = 1122
factor(565) = 5*113
factor(557) = 1+557
557*565 = 314705
So the number could be 314705
At this point in tme I am not convinced that this is the only possible answer though.