Here we will explain what 143 mod 171 means and show how to calculate it. 143 mod 171 is short for 143 modulo 171 and it can also be called 143 modulus 171.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 143 mod 171?" you are asking "What is the Remainder when you divide 143 by 171?".
We will show you two methods of finding 143 mod 171 (143 modulo 171). 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 143 is the Dividend, 171 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 143 mod 171 using the Modulo Method, we first divide the Dividend (143) by the Divisor (171).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (171).
Then finally, we subtract the answer in the second step from the Dividend (143) to get the answer. Here is the math to illustrate how to get 143 mod 171 using our Modulo Method:
143 ÷ 171 ≈ 0.836257
0 × 171 = 0
143 - 0 = 143
Thus, the answer to "What is 143 mod 171?" is 143.
Modulus Method
To find 143 mod 171 using the Modulus Method, we first find the highest multiple of the Divisor (171) that is equal to or less than the Dividend (143).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 143 modulus 171 (143 mod 171):
Multiples of 171 are 0, 171, 342, 513, etc. and the highest multiple of 171 equal to or less than 143 is 0. Therefore, to get the answer:
143 - 0 = 143
Thus, once again, the answer to "What is 143 mod 171?" is 143.
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