Here we will explain what 159 mod 113 means and show how to calculate it. 159 mod 113 is short for 159 modulo 113 and it can also be called 159 modulus 113.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 159 mod 113?" you are asking "What is the Remainder when you divide 159 by 113?".
We will show you two methods of finding 159 mod 113 (159 modulo 113). 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 159 is the Dividend, 113 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 159 mod 113 using the Modulo Method, we first divide the Dividend (159) by the Divisor (113).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (113).
Then finally, we subtract the answer in the second step from the Dividend (159) to get the answer. Here is the math to illustrate how to get 159 mod 113 using our Modulo Method:
159 ÷ 113 ≈ 1.407080
1 × 113 = 113
159 - 113 = 46
Thus, the answer to "What is 159 mod 113?" is 46.
Modulus Method
To find 159 mod 113 using the Modulus Method, we first find the highest multiple of the Divisor (113) that is equal to or less than the Dividend (159).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 159 modulus 113 (159 mod 113):
Multiples of 113 are 0, 113, 226, 339, etc. and the highest multiple of 113 equal to or less than 159 is 113. Therefore, to get the answer:
159 - 113 = 46
Thus, once again, the answer to "What is 159 mod 113?" is 46.
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