# Thread: Number theory, divisibility by 22

1. ## Number theory, divisibility by 22

Hi guys, I'm taking an advanced algebra course and this is one of the question in my assignment.

Q: Decide which of the following integers are divisble by 22.
a)0
b)192544
c)444
d)-32516
e)-195518

I don't know if I can just use the long division to do it or I have to apply the divisibility by 11. Thanks for your help.

2. Originally Posted by suedenation
Hi guys, I'm taking an advanced algebra course and this is one of the question in my assignment.

Q: Decide which of the following integers are divisble by 22.
a)0
b)192544
c)444
d)-32516
e)-195518

I don't know if I can just use the long division to do it or I have to apply the divisibility by 11. Thanks for your help.
Note,
gcd(2,11)=1
Thus, it is equivalent to saying that it is divisible by 2 and by 11.
Note all are even.
Thus, check those that are divisible by 11, how?
Check the alternate sum.
For example,
(b)
4-4+5-2+9-1=11
Which is divisible.

3. Originally Posted by ThePerfectHacker
Note,
gcd(2,11)=1
Thus, it is equivalent to saying that it is divisible by 2 and by 11.
Note all are even.
Thus, check those that are divisible by 11, how?
Check the alternate sum.
For example,
(b)
4-4+5-2+9-1=11
Which is divisible.
Just dividing by 11 also is not rocket science.

RonL

4. Originally Posted by CaptainBlank
Just dividing by 11 also is not rocket science.
??

5. Originally Posted by ThePerfectHacker
??
he meant 22.

Would 0 be considered divisible? (I should know this but I'm too lazy to look it up elsewhere)

6. Originally Posted by Quick
he meant 22.

Would 0 be considered divisible? (I should know this but I'm too lazy to look it up elsewhere)
Yes!
The formal definition of divisibility is that,
a divides b means there exists a k such as,
b=ak
For the integers.

Thus, if we take k=0 then it answers they questions.