Here we will explain what 185 mod 142 means and show how to calculate it. 185 mod 142 is short for 185 modulo 142 and it can also be called 185 modulus 142.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 185 mod 142?" you are asking "What is the Remainder when you divide 185 by 142?".
We will show you two methods of finding 185 mod 142 (185 modulo 142). 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 185 is the Dividend, 142 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 185 mod 142 using the Modulo Method, we first divide the Dividend (185) by the Divisor (142).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (142).
Then finally, we subtract the answer in the second step from the Dividend (185) to get the answer. Here is the math to illustrate how to get 185 mod 142 using our Modulo Method:
185 ÷ 142 ≈ 1.302817
1 × 142 = 142
185 - 142 = 43
Thus, the answer to "What is 185 mod 142?" is 43.
Modulus Method
To find 185 mod 142 using the Modulus Method, we first find the highest multiple of the Divisor (142) that is equal to or less than the Dividend (185).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 185 modulus 142 (185 mod 142):
Multiples of 142 are 0, 142, 284, 426, etc. and the highest multiple of 142 equal to or less than 185 is 142. Therefore, to get the answer:
185 - 142 = 43
Thus, once again, the answer to "What is 185 mod 142?" is 43.
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