Here we will explain what 142 mod 113 means and show how to calculate it. 142 mod 113 is short for 142 modulo 113 and it can also be called 142 modulus 113.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 142 mod 113?" you are asking "What is the Remainder when you divide 142 by 113?".
We will show you two methods of finding 142 mod 113 (142 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 142 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 142 mod 113 using the Modulo Method, we first divide the Dividend (142) 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 (142) to get the answer. Here is the math to illustrate how to get 142 mod 113 using our Modulo Method:
142 ÷ 113 ≈ 1.256637
1 × 113 = 113
142 - 113 = 29
Thus, the answer to "What is 142 mod 113?" is 29.
Modulus Method
To find 142 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 (142).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 142 modulus 113 (142 mod 113):
Multiples of 113 are 0, 113, 226, 339, etc. and the highest multiple of 113 equal to or less than 142 is 113. Therefore, to get the answer:
142 - 113 = 29
Thus, once again, the answer to "What is 142 mod 113?" is 29.
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