15 is a multiple of 5 so when the given number N is divided by 5 we get the same 4 as reminder and the q will be three times when the number N is divided by 15

Remainder when a number is divided by 5

To find the remainder when a number is divided by 5, we need to understand the concept of divisibility and how remainders work.

Divisibility Rule for 5
The divisibility rule for 5 states that a number is divisible by 5 if its units digit is either 0 or 5. In other words, if a number ends in 0 or 5, it is divisible by 5.

Dividing a number by 15
Let's consider a number N that when divided by 15 gives a remainder of 4. Mathematically, we can represent this as N ≡ 4 (mod 15), where "≡" denotes congruence and "mod" represents the modulus.

Understanding Congruence
In modular arithmetic, congruence means that two numbers have the same remainder when divided by a certain modulus. In this case, N and 4 have the same remainder when divided by 15.

Using the Remainder Theorem
The remainder theorem states that if two numbers have the same remainder when divided by a certain divisor, then their difference is divisible by that divisor.

Since N ≡ 4 (mod 15), we can write N = 15k + 4, where k is an integer representing the number of times 15 divides N completely.

Finding the Remainder when N is divided by 5
To find the remainder when N is divided by 5, we substitute the expression for N from the previous step.

N = 15k + 4

When we divide N by 5, we get:

N/5 = (15k + 4)/5

Simplifying the expression further:

N/5 = 3k + 0.8

Since the remainder should be an integer, we can ignore the decimal part and focus on the coefficient of k, which is 3.

Conclusion
The remainder when the number N is divided by 5 is 3.