Here we will explain what 175 mod 21 means and show how to calculate it. 175 mod 21 is short for 175 modulo 21 and it can also be called 175 modulus 21.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 175 mod 21?" you are asking "What is the Remainder when you divide 175 by 21?".
We will show you two methods of finding 175 mod 21 (175 modulo 21). 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 175 is the Dividend, 21 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 175 mod 21 using the Modulo Method, we first divide the Dividend (175) by the Divisor (21).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (21).
Then finally, we subtract the answer in the second step from the Dividend (175) to get the answer. Here is the math to illustrate how to get 175 mod 21 using our Modulo Method:
175 ÷ 21 ≈ 8.333333
8 × 21 = 168
175 - 168 = 7
Thus, the answer to "What is 175 mod 21?" is 7.
Modulus Method
To find 175 mod 21 using the Modulus Method, we first find the highest multiple of the Divisor (21) that is equal to or less than the Dividend (175).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 175 modulus 21 (175 mod 21):
Multiples of 21 are 0, 21, 42, 63, etc. and the highest multiple of 21 equal to or less than 175 is 168. Therefore, to get the answer:
175 - 168 = 7
Thus, once again, the answer to "What is 175 mod 21?" is 7.
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