linear combinations

[mad_mathematician]

how do i use d = rA + sB to find the HCF of A and B, where A = 91 and B = 130

i tried d = 2A - B = 182 - 130 = 52, but thats not right
i tried it with A = 130 and B = 91, so d = A - B = 130 - 91 = 39, but thats not right either

i can get it 2 work 4 A = 24 and B = 42
d = 2A - B = 48 - 42 = 6

A = 27, B = 36

d = 2A - B = 54 - 36 = 18. this doesnt work either, bt if i do A = 36 and B = 27
d = A - B = 36 - 27 = 9, then it works

HELP!

 

[mad_mathematician]

A = 27, B = 36

d = 3A - 2B = 81 - 72 = 9 - that is the HCF of 27 and 36, figured that 1 out

A = 91, B = 130

d = 3A - 2B = 273 - 260 = 13 - that is the HCF of 91 and 130

so i figured out the original prob. i just dont understand how you know what numbers to use like if you dont know what the HCF is and you're actually trying to work it out or whatever.

 

[tkhunny]

It looks like a horrible joke, to me. Why not just use a Prime Factorization and be done with it? No need to search about.