Here we will explain what 166 mod 198 means and show how to calculate it. 166 mod 198 is short for 166 modulo 198 and it can also be called 166 modulus 198.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 166 mod 198?" you are asking "What is the Remainder when you divide 166 by 198?".
We will show you two methods of finding 166 mod 198 (166 modulo 198). 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 166 is the Dividend, 198 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 166 mod 198 using the Modulo Method, we first divide the Dividend (166) by the Divisor (198).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (198).
Then finally, we subtract the answer in the second step from the Dividend (166) to get the answer. Here is the math to illustrate how to get 166 mod 198 using our Modulo Method:
166 ÷ 198 ≈ 0.838384
0 × 198 = 0
166 - 0 = 166
Thus, the answer to "What is 166 mod 198?" is 166.
Modulus Method
To find 166 mod 198 using the Modulus Method, we first find the highest multiple of the Divisor (198) that is equal to or less than the Dividend (166).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 166 modulus 198 (166 mod 198):
Multiples of 198 are 0, 198, 396, 594, etc. and the highest multiple of 198 equal to or less than 166 is 0. Therefore, to get the answer:
166 - 0 = 166
Thus, once again, the answer to "What is 166 mod 198?" is 166.
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