0 votes
41 views
$\gcd(36,k)=6$, then what is the k?

I know the only naive method,can anyone explain any other method.

edited | 41 views

## 1 Answer

0 votes
Why naive method?

Its straight forward that gcd is 6, that means whatever be the number that must the product of 2 smallest primes. Hence 6 is clearly the answer

But if you keep on increasing the multiple of 6 then you won’t get GCD as 6, then GCD would get mulitplied by 2 and 3
by (356 points)
0
I know the method like this

$36=2 \times {\color{Red}{2 \times 3} } \times 3$

$6={\color{Red}{2 \times 3 } }$

Less than can’t be possible and multiple of $’6’$  which is less than or equal to $’36’$  is also not possible because $36$ is a multiple of $6$.

So, $k=6,42$ is possible.
0
int gcd(int a, int b)
{

if  (a == 0)
return b;
if (b == 0)
return a;

if (a == b)
return a;

if (a > b)
return gcd(a-b, b);
return gcd
}


Here we can put 36 and 6 as two elements $a$ and $b$. It will give the other number

+2
K can be 42 also :(
0
Yes, you are right, I missed that one.

any other possibilities are there?
+2
36*i+ 6 for all i > 0
0
Can be write $i\geq 0?$
0
if $\gcd (48,k) = 6$

then $k=48\times i + 6\:\:\forall i \geq 0$

it is right?