Here we will explain what 197 mod 138 means and show how to calculate it. 197 mod 138 is short for 197 modulo 138 and it can also be called 197 modulus 138.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 197 mod 138?" you are asking "What is the Remainder when you divide 197 by 138?".
We will show you two methods of finding 197 mod 138 (197 modulo 138). 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 197 is the Dividend, 138 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 197 mod 138 using the Modulo Method, we first divide the Dividend (197) by the Divisor (138).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (138).
Then finally, we subtract the answer in the second step from the Dividend (197) to get the answer. Here is the math to illustrate how to get 197 mod 138 using our Modulo Method:
197 ÷ 138 ≈ 1.427536
1 × 138 = 138
197 - 138 = 59
Thus, the answer to "What is 197 mod 138?" is 59.
Modulus Method
To find 197 mod 138 using the Modulus Method, we first find the highest multiple of the Divisor (138) that is equal to or less than the Dividend (197).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 197 modulus 138 (197 mod 138):
Multiples of 138 are 0, 138, 276, 414, etc. and the highest multiple of 138 equal to or less than 197 is 138. Therefore, to get the answer:
197 - 138 = 59
Thus, once again, the answer to "What is 197 mod 138?" is 59.
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