Here we will explain what 103 mod 20 means and show how to calculate it. 103 mod 20 is short for 103 modulo 20 and it can also be called 103 modulus 20.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 103 mod 20?" you are asking "What is the Remainder when you divide 103 by 20?".
We will show you two methods of finding 103 mod 20 (103 modulo 20). 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, 20 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 20 using the Modulo Method, we first divide the Dividend (103) by the Divisor (20).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (20).
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 20 using our Modulo Method:
103 ÷ 20 = 5.15
5 × 20 = 100
103 - 100 = 3
Thus, the answer to "What is 103 mod 20?" is 3.
Modulus Method
To find 103 mod 20 using the Modulus Method, we first find the highest multiple of the Divisor (20) 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 20 (103 mod 20):
Multiples of 20 are 0, 20, 40, 60, etc. and the highest multiple of 20 equal to or less than 103 is 100. Therefore, to get the answer:
103 - 100 = 3
Thus, once again, the answer to "What is 103 mod 20?" is 3.
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