Here we will explain what 166 mod 11 means and show how to calculate it. 166 mod 11 is short for 166 modulo 11 and it can also be called 166 modulus 11.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 166 mod 11?" you are asking "What is the Remainder when you divide 166 by 11?".
We will show you two methods of finding 166 mod 11 (166 modulo 11). 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, 11 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 11 using the Modulo Method, we first divide the Dividend (166) by the Divisor (11).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (11).
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 11 using our Modulo Method:
166 ÷ 11 ≈ 15.090909
15 × 11 = 165
166 - 165 = 1
Thus, the answer to "What is 166 mod 11?" is 1.
Modulus Method
To find 166 mod 11 using the Modulus Method, we first find the highest multiple of the Divisor (11) 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 11 (166 mod 11):
Multiples of 11 are 0, 11, 22, 33, etc. and the highest multiple of 11 equal to or less than 166 is 165. Therefore, to get the answer:
166 - 165 = 1
Thus, once again, the answer to "What is 166 mod 11?" is 1.
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