Here we will explain what 161 mod 165 means and show how to calculate it. 161 mod 165 is short for 161 modulo 165 and it can also be called 161 modulus 165.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 161 mod 165?" you are asking "What is the Remainder when you divide 161 by 165?".
We will show you two methods of finding 161 mod 165 (161 modulo 165). 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 161 is the Dividend, 165 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 161 mod 165 using the Modulo Method, we first divide the Dividend (161) by the Divisor (165).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (165).
Then finally, we subtract the answer in the second step from the Dividend (161) to get the answer. Here is the math to illustrate how to get 161 mod 165 using our Modulo Method:
161 ÷ 165 ≈ 0.975758
0 × 165 = 0
161 - 0 = 161
Thus, the answer to "What is 161 mod 165?" is 161.
Modulus Method
To find 161 mod 165 using the Modulus Method, we first find the highest multiple of the Divisor (165) that is equal to or less than the Dividend (161).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 161 modulus 165 (161 mod 165):
Multiples of 165 are 0, 165, 330, 495, etc. and the highest multiple of 165 equal to or less than 161 is 0. Therefore, to get the answer:
161 - 0 = 161
Thus, once again, the answer to "What is 161 mod 165?" is 161.
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