Question

Prove: if a|b and a>0, then (a,b)=a

Answer 1

(a,b) stands for gcd(a,b), correct?

What is the definition you're given of gcd? I just want to make sure it matches the one I'm using.

Answer 2

yes

Answer 3

gcd(a,b) means d|a and d|b

Answer 4

if a divide b (a|b) , a is a multiple of b, so you can write a = cb (c time b) where c is a constant., from there you can conclude that gcd(a,b) = a

Answer 5

in this case your d = cb = a

Answer 6

instead of a = cb.. shouldn't it be b = ac since a|b?

Answer 7

how about the fact that a>0?

Answer 8

i am not familiar with the notation a|b ...read a divide b...if a is larger then a = cb, if b is larger then b = ca ..., one of those is right...because i learned maths from a country different than the US

Answer 9

a divides b means b is the larger one.. so b = ac

Answer 10

ok so b = ac , so gcd(a,b) = gcd(a,ac) = a , right? , i don't know why is the condition a > 0, for me, i would think condition is a not equal to zero since a is in the denominator, it can't be zero...

Answer 11

yeah you're right..

Answer 12

thank you so much

Answer 13

np, enjoy :)