Here we will explain what 103 mod 18 means and show how to calculate it. 103 mod 18 is short for 103 modulo 18 and it can also be called 103 modulus 18.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 103 mod 18?" you are asking "What is the Remainder when you divide 103 by 18?".
We will show you two methods of finding 103 mod 18 (103 modulo 18). 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, 18 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 18 using the Modulo Method, we first divide the Dividend (103) by the Divisor (18).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (18).
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 18 using our Modulo Method:
103 ÷ 18 ≈ 5.722222
5 × 18 = 90
103 - 90 = 13
Thus, the answer to "What is 103 mod 18?" is 13.
Modulus Method
To find 103 mod 18 using the Modulus Method, we first find the highest multiple of the Divisor (18) 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 18 (103 mod 18):
Multiples of 18 are 0, 18, 36, 54, etc. and the highest multiple of 18 equal to or less than 103 is 90. Therefore, to get the answer:
103 - 90 = 13
Thus, once again, the answer to "What is 103 mod 18?" is 13.
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