How can I find all the natural numbers x and y as x+y=336 and the highest common divisor (x;y) =24? ▾

Question

i need help about this i am not so good in maths 

Answer 1

x+y=336 and the GCF of x and y is 24

24x+24y=336 and x and y are relatively prime (they have no common factors other than 1)

24(x+y)=336

divide both sides by 24

x+y=14

x=1, y=13, 24+312=336

x=2, y=12 cannot be used because the GCF would be 48

x=3, y=11, 72+264=336

x=4, y=10 cannot be used because the GCF would be 48

x=5, y=9, 120+216=336

x=6, y=8, cannot be used because the GCF would be 48

x=7, y=7, cannot be used because the GCF would be 168

x=8, y=6 and so on are just repeats of the previous numbers except in reverse order