# Division of whole numbers [closed]

Is there any certain formula to figure out a problem like 9_8_7_ is divisible by 44 but not by 4? This is not a real question just similar to one I have seen. I realize that anything divisible by 44 will be divisible by 4, I do not need to find an answer to the problem I am trying to see if there is a faster way than trying all numbers in all situations! Thank you!

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If you really said that some number can be divided by 44 but not by 4, then I suggest you get more comfortable with the concept of divisibility. o_o – Josué Molina Feb 28 '12 at 23:18
I know that the number would be divisible by both but I put that because I do not need an answer. I am just trying to figure out if there is a formula or a rule that would help solve a problem like this faster than using each number in every spot. – SNS Feb 28 '12 at 23:28
In general, I think the fastest algorithm to determine whether or not one number is divisible by another is long division. For a small divisor, these rules may help: en.wikipedia.org/wiki/Divisibility_rule If you want to find every number that a given number is divisible by, what you're after is a factoring algorithm. I think the only simple factoring algorithm is to simply try dividing by every prime number, but for what it's worth, here's Wikipedia's article: en.wikipedia.org/wiki/Integer_factorization – Tanner Swett Feb 28 '12 at 23:50
"This is not a real question" ... hmm, there's a flag for that. – The Chaz 2.0 Feb 29 '12 at 0:21
@TheChaz I am sorry if you think there is something wrong with my question but it is not a homework question or anything it is just a question I have encountered before and I am studying for a final and would like to know before I take it if there is an easier way to find the answers. Flag all you want but you don't have to be rude. – SNS Feb 29 '12 at 2:18

## closed as not a real question by Brandon Carter, Kannappan Sampath, Asaf Karagila, J. M., t.b.Mar 24 '12 at 16:05

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.

Every number divisible by $44$ is also divisible by $4$. To see this, consider a number $n$ divisible by $44$. This means that we can write $n$ as: $$n = 44k$$ where $k$ is some integer. Now factor $44$ further, we get: $$n = 4\times 11\times k = 2\times 2\times 11\times k.$$ Obviously, $n$ is divisible by $4$ (also by $2$, $11$, and $22$).
I think you are looking for "modular arithmetic." If you want to determine if a number is divisible by $n$, then you want to determine if that number is congruent to $0$ mod $n$. Methods for doing this depend on $n$. Your question is far to general to have any sort of formula or specific trick.
In fact, it is impossible to tell if $4$ divides a number of the form 9_8_7_ without knowing the last digit, but it will be divisible by $4$ iff the last digit is $2$ or $6$. This is because $4$ divides $20$ and in turn $100$, so first of all we only need to look at the last two digits, and secondly we only need to consider that last two digits mod $20$. Specifically, 9_8_7x is congruent to $1x$ mod 20, and the only numbers divisible by $4$ in the teens are $12$ and $16$.