if G.C.D. of two numbers is 43 and the product of uncommon factor is 21

Question

Then the smaller number is?

Answer 1

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Answer 2

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