Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Just tried googling but couldn't find any example, but how 3 % 5 = 3

Googled it

share|improve this question
If you count $1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,\ldots$, what is the third number that comes up? –  Michael Greinecker Sep 12 '12 at 10:30
When you divide $3$ by $5$, the remainder is $3$. –  Joe Johnson 126 Sep 12 '12 at 10:31
Also, $3 \equiv 3 \mod 5$, because $3-3=0 \equiv 0 \mod 5$. –  Andrea Orta Sep 12 '12 at 10:34
If you are asking this question $\implies$ you need to look at the definition of modulo operation. see en.wikipedia.org/wiki/Modulo_operation –  Aang Sep 12 '12 at 12:45

6 Answers 6

up vote 11 down vote accepted

If $a$ and $b$ are positive integers, there exist unique integers $q$, $r$ with $$a = bq + r$$ and $0 \leq r < b$.

This theorem is called the division algorithm, and $a\ \%\ b$ is defined to be this $r$. In your case, $3 = 0\cdot5 + 3$ and $0 \leq 3 < 5$, so the answer is 3.

share|improve this answer

$a \equiv b \, (\text{mod} c)$ means $a-b$ is divisible by $c$. [Definition]

Since $3 - 3 = 0$ is divisible by $5$, we have $3 \equiv 3 \, (\text{mod} 5)$.

share|improve this answer

hmmm Actually Mod (%) returns the remainder Given two positive numbers, a (the dividend) and b (the divisor), a modulus % is the remainder of the Euclidean division of a by b. For instance, the expression "9 mod 8" would evaluate to 1 because 9divided by 8 leaves a remainder of 1, while "9 mod 3" would evaluate to 0 because the division of 9 by 3 leaves a remainder of 0. hope this will help you cheers

share|improve this answer
plus if your dividend if less than the divisor, then your remainder will be the dividend :) –  Ali Sep 12 '12 at 10:52
It works for negative numbers too, unless you are using a non-standard definition on Mod? –  user1729 Sep 12 '12 at 13:02

a modulo b = r Where r is the remainder of the division a by b => a = b*q + r where q is the quotient of the division a/b.

For example: 9 modulo 4 = 1 and the quotient is 2

i.e 9 = (4*2) + 1

In a similar fashion: 3 modulo 5 = 3 and the quotient is 0- =>3=(5*0)+3

share|improve this answer

in general if a is less than b then a%b= a

so this implies that 3%5=3 and 6%7=6. another way of viewing this is by reading the statement a%b as "how many object remains if we SUCCESSIVELY take "b" objects from a bag with "a" objects untill we CAN'T TAKE ANYMORE!". Having that in mind 5%2 mean that we successively take 2 objects from a bag containing 5 objects. 1st we will take the 2 objects and leaving behind 3 objects, then we take another 2 object leaving behing 1 object in the bag, since we can't take 2 objects any more, SINCE there is only one remaining hence 5%2=1. applying the same analogy and solving for 3%5 we initially have 3 object in a bag and we want to successively take 5 objects. but we cant since the are insufficient objects in the bag so we can't take any objects and hence 3 objects will remain, this implies that 3%5=3.

hope this helps.

share|improve this answer
Check out the following link to help format questions/answers. –  Vincent Oct 21 '14 at 16:13
The only answer that actually made sense. When people ask these kinds of questions, it's because of a lack of training in mathematics and the last thing they need are mathematicians trying to explain things with more math. Thanks for breaking it down to simple terms! :) –  kirk.burleson Jul 19 at 16:21

by definition, the remainder of a division is the fractional part of a division. if you have 3/5 (3 divided by 5), you have the fractional part represented as 3/5. since a remainder is the dividend or numerator of a fraction, you just take 3 as your remainder (the divisor or denominator is not mentioned in the remainder).
therefore, 3 % 5 = 3.

just like 5 % 3 = dividing 5 by 3, you get 1 and 2/5. to get the remainder part, you know that 2 is the numerator so 2 is the remainder (the denominator, 5, is not mentioned in the remainder).

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.