Here we will explain what 180 mod 168 means and show how to calculate it. 180 mod 168 is short for 180 modulo 168 and it can also be called 180 modulus 168.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 180 mod 168?" you are asking "What is the Remainder when you divide 180 by 168?".
We will show you two methods of finding 180 mod 168 (180 modulo 168). 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 180 is the Dividend, 168 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 180 mod 168 using the Modulo Method, we first divide the Dividend (180) by the Divisor (168).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (168).
Then finally, we subtract the answer in the second step from the Dividend (180) to get the answer. Here is the math to illustrate how to get 180 mod 168 using our Modulo Method:
180 ÷ 168 ≈ 1.071429
1 × 168 = 168
180 - 168 = 12
Thus, the answer to "What is 180 mod 168?" is 12.
Modulus Method
To find 180 mod 168 using the Modulus Method, we first find the highest multiple of the Divisor (168) that is equal to or less than the Dividend (180).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 180 modulus 168 (180 mod 168):
Multiples of 168 are 0, 168, 336, 504, etc. and the highest multiple of 168 equal to or less than 180 is 168. Therefore, to get the answer:
180 - 168 = 12
Thus, once again, the answer to "What is 180 mod 168?" is 12.
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