For A to be correct, I would have thought it would be worded "every unique prime factor of s is also a unique prime factor of r" or "every different prime factor..."
But, I misinterpreted the statement, because the factors for a number, say 18, are all possible combinations of its prime factors, 2^1 * 3^2: 1, [2], [3], 6, 9, 18. The prime numbers only ever appear here once.
Thus:
Statement 2) If every prime factor of s is also a prime factor of r,
s could be 2^100 * 3^100 * 7^100
and r = 2 * 3 * 7
They would share the same prime factors:
r: 1, [2], [3], 6, [7], 14, 21, 42
s: 1, [2], [3], 4, 6, [7], 8, 9, 12, ...
r/s = 1/(2^99) * 1/(3^99) * 1/(7^99), definitely not an integer.
Last edited by
goalevan on Sun Jul 17, 2011 5:02 pm, edited 1 time in total.
