A number theory problem by A Former Brilliant Member
The sum of 2 positive integers and is 52, and their lowest common multiple is 168.
Find the value of .
The answer is 4.
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1 solution
Taking 1 6 8 = 2 3 3 1 7 1 , it has positive integer divisors: 1 , 2 , 3 , 4 , 6 , 7 , 8 , 1 2 , 1 4 , 2 1 , 2 4 , 2 8 , 4 2 , 5 6 , 8 4 , 1 6 8 . Of these divisors, 2 4 + 2 8 = 5 2 . Hence ∣ 2 4 − 2 8 ∣ = 4 .