Here we will explain what 108 mod 3 means and show how to calculate it. 108 mod 3 is short for 108 modulo 3 and it can also be called 108 modulus 3.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 108 mod 3?" you are asking "What is the Remainder when you divide 108 by 3?".
We will show you two methods of finding 108 mod 3 (108 modulo 3). To differentiate our methods, we will call them the "Modulo Method" and the "Modulus Method".
Before we continue, we remind you of what the different parts of a division problem are called so you can follow along: Dividend / Divisor = Quotient and in this case 108 is the Dividend, 3 is the Divisor, and the answer is called the Quotient.
Furthermore, the Quotient x.y has two parts: x to the left of the decimal point is the Whole part, and y to the right of the decimal point is the Fractional part.
Modulo Method
To find 108 mod 3 using the Modulo Method, we first divide the Dividend (108) by the Divisor (3).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (3).
Then finally, we subtract the answer in the second step from the Dividend (108) to get the answer. Here is the math to illustrate how to get 108 mod 3 using our Modulo Method:
108 ÷ 3 = 36
36 × 3 = 108
108 - 108 = 0
Thus, the answer to "What is 108 mod 3?" is 0.
Modulus Method
To find 108 mod 3 using the Modulus Method, we first find the highest multiple of the Divisor (3) that is equal to or less than the Dividend (108).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 108 modulus 3 (108 mod 3):
Multiples of 3 are 0, 3, 6, 9, etc. and the highest multiple of 3 equal to or less than 108 is 108. Therefore, to get the answer:
108 - 108 = 0
Thus, once again, the answer to "What is 108 mod 3?" is 0.
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