Here we will explain what 144 mod 19 means and show how to calculate it. 144 mod 19 is short for 144 modulo 19 and it can also be called 144 modulus 19.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 144 mod 19?" you are asking "What is the Remainder when you divide 144 by 19?".
We will show you two methods of finding 144 mod 19 (144 modulo 19). 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 144 is the Dividend, 19 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 144 mod 19 using the Modulo Method, we first divide the Dividend (144) by the Divisor (19).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (19).
Then finally, we subtract the answer in the second step from the Dividend (144) to get the answer. Here is the math to illustrate how to get 144 mod 19 using our Modulo Method:
144 ÷ 19 ≈ 7.578947
7 × 19 = 133
144 - 133 = 11
Thus, the answer to "What is 144 mod 19?" is 11.
Modulus Method
To find 144 mod 19 using the Modulus Method, we first find the highest multiple of the Divisor (19) that is equal to or less than the Dividend (144).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 144 modulus 19 (144 mod 19):
Multiples of 19 are 0, 19, 38, 57, etc. and the highest multiple of 19 equal to or less than 144 is 133. Therefore, to get the answer:
144 - 133 = 11
Thus, once again, the answer to "What is 144 mod 19?" is 11.
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