Here we will explain what 18 mod 189 means and show how to calculate it. 18 mod 189 is short for 18 modulo 189 and it can also be called 18 modulus 189.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 18 mod 189?" you are asking "What is the Remainder when you divide 18 by 189?".
We will show you two methods of finding 18 mod 189 (18 modulo 189). 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 18 is the Dividend, 189 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 18 mod 189 using the Modulo Method, we first divide the Dividend (18) by the Divisor (189).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (189).
Then finally, we subtract the answer in the second step from the Dividend (18) to get the answer. Here is the math to illustrate how to get 18 mod 189 using our Modulo Method:
18 ÷ 189 ≈ 0.095238
0 × 189 = 0
18 - 0 = 18
Thus, the answer to "What is 18 mod 189?" is 18.
Modulus Method
To find 18 mod 189 using the Modulus Method, we first find the highest multiple of the Divisor (189) that is equal to or less than the Dividend (18).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 18 modulus 189 (18 mod 189):
Multiples of 189 are 0, 189, 378, 567, etc. and the highest multiple of 189 equal to or less than 18 is 0. Therefore, to get the answer:
18 - 0 = 18
Thus, once again, the answer to "What is 18 mod 189?" is 18.
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