Here we will explain what 168 mod 197 means and show how to calculate it. 168 mod 197 is short for 168 modulo 197 and it can also be called 168 modulus 197.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 168 mod 197?" you are asking "What is the Remainder when you divide 168 by 197?".
We will show you two methods of finding 168 mod 197 (168 modulo 197). 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 168 is the Dividend, 197 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 168 mod 197 using the Modulo Method, we first divide the Dividend (168) by the Divisor (197).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (197).
Then finally, we subtract the answer in the second step from the Dividend (168) to get the answer. Here is the math to illustrate how to get 168 mod 197 using our Modulo Method:
168 ÷ 197 ≈ 0.852792
0 × 197 = 0
168 - 0 = 168
Thus, the answer to "What is 168 mod 197?" is 168.
Modulus Method
To find 168 mod 197 using the Modulus Method, we first find the highest multiple of the Divisor (197) that is equal to or less than the Dividend (168).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 168 modulus 197 (168 mod 197):
Multiples of 197 are 0, 197, 394, 591, etc. and the highest multiple of 197 equal to or less than 168 is 0. Therefore, to get the answer:
168 - 0 = 168
Thus, once again, the answer to "What is 168 mod 197?" is 168.
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