How is $3\equiv 3\bmod{5}$ Just tried googling but couldn't find any example, but how $3\equiv 3\bmod{5}$
Googled it
 A: $a \equiv b \, (\text{mod} c)$ means $a-b$ is divisible by $c$. [Definition]
Since $3 - 3 = 0$ is divisible by $5$, we have $3 \equiv 3 \, (\text{mod} 5)$.
A: 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.
A: 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.
A: 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
A: 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
A: 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).
