The term “mod” stands for modulo, which is a mathematical operation that finds the remainder when one number is divided by another. In this case, we want to calculate 1 mod 3.
To perform this operation, we divide 1 by 3. Since 1 is less than 3, it does not fully divide into 3. The quotient of 1 divided by 3 is 0, indicating that 3 fits into 1 zero times. Therefore, we now calculate the remainder:
- 0 * 3 = 0 (this is the largest multiple of 3 that is less than or equal to 1)
- 1 – 0 = 1 (this gives us the remainder)
Thus, the result of 1 mod 3 is 1. In simpler terms, when you have 1 and you try to divide it by 3, you cannot take away 3, which means you are left with the original number, 1.
This operation can be quite useful in various programming and mathematical scenarios, especially when dealing with cycles or periodicity, as it allows us to determine how numbers behave within certain bounds.