Here we will explain what 117 mod 178 means and show how to calculate it. 117 mod 178 is short for 117 modulo 178 and it can also be called 117 modulus 178.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 117 mod 178?" you are asking "What is the Remainder when you divide 117 by 178?".
We will show you two methods of finding 117 mod 178 (117 modulo 178). 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 117 is the Dividend, 178 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 117 mod 178 using the Modulo Method, we first divide the Dividend (117) by the Divisor (178).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (178).
Then finally, we subtract the answer in the second step from the Dividend (117) to get the answer. Here is the math to illustrate how to get 117 mod 178 using our Modulo Method:
117 ÷ 178 ≈ 0.657303
0 × 178 = 0
117 - 0 = 117
Thus, the answer to "What is 117 mod 178?" is 117.
Modulus Method
To find 117 mod 178 using the Modulus Method, we first find the highest multiple of the Divisor (178) that is equal to or less than the Dividend (117).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 117 modulus 178 (117 mod 178):
Multiples of 178 are 0, 178, 356, 534, etc. and the highest multiple of 178 equal to or less than 117 is 0. Therefore, to get the answer:
117 - 0 = 117
Thus, once again, the answer to "What is 117 mod 178?" is 117.
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