Here we will explain what 150 mod 117 means and show how to calculate it. 150 mod 117 is short for 150 modulo 117 and it can also be called 150 modulus 117.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 150 mod 117?" you are asking "What is the Remainder when you divide 150 by 117?".
We will show you two methods of finding 150 mod 117 (150 modulo 117). 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 150 is the Dividend, 117 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 150 mod 117 using the Modulo Method, we first divide the Dividend (150) by the Divisor (117).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (117).
Then finally, we subtract the answer in the second step from the Dividend (150) to get the answer. Here is the math to illustrate how to get 150 mod 117 using our Modulo Method:
150 ÷ 117 ≈ 1.282051
1 × 117 = 117
150 - 117 = 33
Thus, the answer to "What is 150 mod 117?" is 33.
Modulus Method
To find 150 mod 117 using the Modulus Method, we first find the highest multiple of the Divisor (117) that is equal to or less than the Dividend (150).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 150 modulus 117 (150 mod 117):
Multiples of 117 are 0, 117, 234, 351, etc. and the highest multiple of 117 equal to or less than 150 is 117. Therefore, to get the answer:
150 - 117 = 33
Thus, once again, the answer to "What is 150 mod 117?" is 33.
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