Starting with the 'product of uncommon factors is 21', the factors of 21 are
1,3,7,21 (http://statsfiddle.info/Primes/AllFactors/21)
So the uncommon factors could be 1 & 21 or 3 & 7. Noting that 1 is generally excluded from factorization, as it is common to all numbers, which leaves 3 & 7.
Since GCD is determined as the largest number common to two numbers, we can multiply our 'uncommon' factors by the GCD to return the original numbers:
3 x 43 = 129
7 x 43 = 301
Which you can then check your work by finding the GCD(129, 301) here: http://statsfiddle.info/Primes/GreatestCommonDivisor/129?number2=301