Simple Common Factor query

Question

if $a|b$ and $a|c$, does it mean that $b|c$?

No. Let $b=ak$, $c=am$ with $k>m\ge 1$. – user236182 Jan 01 '16 at 20:21 — user236182, Jan 01 '16 at 20:21

score 3 · Accepted Answer · answered Jan 01 '16 at 20:14

3

No, consider $3|9$ and $3|15$ but $9$ does not divide $15$.

answered Jan 01 '16 at 20:14

Gregory Grant

is there any way to link the two together with a common divisor? GCD not known? Because I want to show $b|c$ and only have that information? For example $b|kc$ where $k$ is an integer? – LucasCK Jan 01 '16 at 20:16
Yes you can say that $a|b$ and $a|c$ implies $a|gcd(b,c)$. That's about the best you can say. – Gregory Grant Jan 01 '16 at 20:18
I see, i have edit my comment a little bit can u inform what u think? – LucasCK Jan 01 '16 at 20:19
I'm afraid the most you can possibly conclude if all you know is $a|b$ and $a|c$ is that $a|gcd(b,c)$. You would need more information to say something stronger than that. – Gregory Grant Jan 01 '16 at 20:22
ok, thank u v much – LucasCK Jan 01 '16 at 20:22
You're welcome :-) – Gregory Grant Jan 01 '16 at 20:23
$a\mid b$ and $a\mid c$ is equivalent to $a\mid \gcd(b,c)$ (not only implied). – user236182 Jan 01 '16 at 20:23
@user236182 Ok true. – Gregory Grant Jan 01 '16 at 20:51

score 0 · Answer 2 · answered Jan 01 '16 at 20:17

0

No, for example $2|6$ and $2|10$ but $6\nmid10$.

answered Jan 01 '16 at 20:17

3SAT

2 Answers2