Here we will explain what 107 mod 189 means and show how to calculate it. 107 mod 189 is short for 107 modulo 189 and it can also be called 107 modulus 189.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 107 mod 189?" you are asking "What is the Remainder when you divide 107 by 189?".
We will show you two methods of finding 107 mod 189 (107 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 107 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 107 mod 189 using the Modulo Method, we first divide the Dividend (107) 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 (107) to get the answer. Here is the math to illustrate how to get 107 mod 189 using our Modulo Method:
107 ÷ 189 ≈ 0.566138
0 × 189 = 0
107 - 0 = 107
Thus, the answer to "What is 107 mod 189?" is 107.
Modulus Method
To find 107 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 (107).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 107 modulus 189 (107 mod 189):
Multiples of 189 are 0, 189, 378, 567, etc. and the highest multiple of 189 equal to or less than 107 is 0. Therefore, to get the answer:
107 - 0 = 107
Thus, once again, the answer to "What is 107 mod 189?" is 107.
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