Here we will explain what 160 mod 38 means and show how to calculate it. 160 mod 38 is short for 160 modulo 38 and it can also be called 160 modulus 38.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 160 mod 38?" you are asking "What is the Remainder when you divide 160 by 38?".
We will show you two methods of finding 160 mod 38 (160 modulo 38). 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 160 is the Dividend, 38 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 160 mod 38 using the Modulo Method, we first divide the Dividend (160) by the Divisor (38).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (38).
Then finally, we subtract the answer in the second step from the Dividend (160) to get the answer. Here is the math to illustrate how to get 160 mod 38 using our Modulo Method:
160 ÷ 38 ≈ 4.210526
4 × 38 = 152
160 - 152 = 8
Thus, the answer to "What is 160 mod 38?" is 8.
Modulus Method
To find 160 mod 38 using the Modulus Method, we first find the highest multiple of the Divisor (38) that is equal to or less than the Dividend (160).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 160 modulus 38 (160 mod 38):
Multiples of 38 are 0, 38, 76, 114, etc. and the highest multiple of 38 equal to or less than 160 is 152. Therefore, to get the answer:
160 - 152 = 8
Thus, once again, the answer to "What is 160 mod 38?" is 8.
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