Here we will explain what 103 mod 123 means and show how to calculate it. 103 mod 123 is short for 103 modulo 123 and it can also be called 103 modulus 123.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 103 mod 123?" you are asking "What is the Remainder when you divide 103 by 123?".
We will show you two methods of finding 103 mod 123 (103 modulo 123). 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 103 is the Dividend, 123 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 103 mod 123 using the Modulo Method, we first divide the Dividend (103) by the Divisor (123).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (123).
Then finally, we subtract the answer in the second step from the Dividend (103) to get the answer. Here is the math to illustrate how to get 103 mod 123 using our Modulo Method:
103 ÷ 123 ≈ 0.837398
0 × 123 = 0
103 - 0 = 103
Thus, the answer to "What is 103 mod 123?" is 103.
Modulus Method
To find 103 mod 123 using the Modulus Method, we first find the highest multiple of the Divisor (123) that is equal to or less than the Dividend (103).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 103 modulus 123 (103 mod 123):
Multiples of 123 are 0, 123, 246, 369, etc. and the highest multiple of 123 equal to or less than 103 is 0. Therefore, to get the answer:
103 - 0 = 103
Thus, once again, the answer to "What is 103 mod 123?" is 103.
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