Here we will explain what 19 mod 6 means and show how to calculate it. 19 mod 6 is short for 19 modulo 6 and it can also be called 19 modulus 6.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 19 mod 6?" you are asking "What is the Remainder when you divide 19 by 6?".
We will show you two methods of finding 19 mod 6 (19 modulo 6). 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 19 is the Dividend, 6 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 19 mod 6 using the Modulo Method, we first divide the Dividend (19) by the Divisor (6).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (6).
Then finally, we subtract the answer in the second step from the Dividend (19) to get the answer. Here is the math to illustrate how to get 19 mod 6 using our Modulo Method:
19 ÷ 6 ≈ 3.166667
3 × 6 = 18
19 - 18 = 1
Thus, the answer to "What is 19 mod 6?" is 1.
Modulus Method
To find 19 mod 6 using the Modulus Method, we first find the highest multiple of the Divisor (6) that is equal to or less than the Dividend (19).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 19 modulus 6 (19 mod 6):
Multiples of 6 are 0, 6, 12, 18, etc. and the highest multiple of 6 equal to or less than 19 is 18. Therefore, to get the answer:
19 - 18 = 1
Thus, once again, the answer to "What is 19 mod 6?" is 1.
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