If a number is expressed as 5k + 3, where k is an integer, what is the remainder

If a number is expressed as 5k + 3, where k is an integer, what is the remainder when this number is divided by 5?

If a number is expressed as 5k + 3, where k is an integer, what is the remainder when this number is divided by 5?

Step 1: Understand the expression 5k + 3. Here, 'k' is any whole number (integer).
Step 2: Recognize that 5k means 5 times some integer 'k'. This part (5k) is always divisible by 5.
Step 3: When we divide 5k by 5, the result is an integer with no remainder.
Step 4: Now, look at the '+ 3' part of the expression. This means we are adding 3 to the result of 5k.
Step 5: When we divide the entire expression (5k + 3) by 5, the 5k part gives us no remainder, and we only need to consider the '+ 3'.
Step 6: The remainder when 3 is divided by 5 is simply 3, because 3 is less than 5.

Modular Arithmetic – Understanding how to find remainders when dividing numbers.
Integer Properties – Recognizing that multiples of a number (like 5k) are divisible by that number.