SOLUTION: A positive integer is 14 more than 21 times another. Their product is 6307. Find the two integers.

Question 1008565: A positive integer is 14 more than 21 times another. Their product is 6307. Find the two integers.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
THE UNEXPECTED SOLUTION:
has just 3 prime factors,
each with an exponent of in the prime factorization.
Therefore has
factors,
making the pairs of factors listed below.

.
Obviously is a lot less than 21 times ,
and is a lot more than 14 more than 21 times ,
so the answer must be and .
Let's check, just in case it could be a trick question:
, so it works.

THE EXPECTED SOLUTION:
= the fist (smaller) number (positive integer) they are talking about
= the other number = 14 more than 21 times the first number
= the product of the two numbers
We need to solve the quadratic equation
<-->
It can be simplified by dividing both sides of the equal sign by ;
<--><--><-->
Solving by factoring:
We look for factors of that add up to .
and add up to , so we re-write the equation as
and factor by parts
-->-->-->--> .
Since was a positive integer, is not a solution to the problem.
and are the two integers.
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