Here we will explain what 17 mod 153 means and show how to calculate it. 17 mod 153 is short for 17 modulo 153 and it can also be called 17 modulus 153.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 17 mod 153?" you are asking "What is the Remainder when you divide 17 by 153?".
We will show you two methods of finding 17 mod 153 (17 modulo 153). 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 17 is the Dividend, 153 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 17 mod 153 using the Modulo Method, we first divide the Dividend (17) by the Divisor (153).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (153).
Then finally, we subtract the answer in the second step from the Dividend (17) to get the answer. Here is the math to illustrate how to get 17 mod 153 using our Modulo Method:
17 ÷ 153 ≈ 0.111111
0 × 153 = 0
17 - 0 = 17
Thus, the answer to "What is 17 mod 153?" is 17.
Modulus Method
To find 17 mod 153 using the Modulus Method, we first find the highest multiple of the Divisor (153) that is equal to or less than the Dividend (17).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 17 modulus 153 (17 mod 153):
Multiples of 153 are 0, 153, 306, 459, etc. and the highest multiple of 153 equal to or less than 17 is 0. Therefore, to get the answer:
17 - 0 = 17
Thus, once again, the answer to "What is 17 mod 153?" is 17.
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