Here we will explain what 144 mod 14 means and show how to calculate it. 144 mod 14 is short for 144 modulo 14 and it can also be called 144 modulus 14.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 144 mod 14?" you are asking "What is the Remainder when you divide 144 by 14?".
We will show you two methods of finding 144 mod 14 (144 modulo 14). 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, 14 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 14 using the Modulo Method, we first divide the Dividend (144) by the Divisor (14).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (14).
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 14 using our Modulo Method:
144 ÷ 14 ≈ 10.285714
10 × 14 = 140
144 - 140 = 4
Thus, the answer to "What is 144 mod 14?" is 4.
Modulus Method
To find 144 mod 14 using the Modulus Method, we first find the highest multiple of the Divisor (14) 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 14 (144 mod 14):
Multiples of 14 are 0, 14, 28, 42, etc. and the highest multiple of 14 equal to or less than 144 is 140. Therefore, to get the answer:
144 - 140 = 4
Thus, once again, the answer to "What is 144 mod 14?" is 4.
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