Here we will explain what 107 mod 3 means and show how to calculate it. 107 mod 3 is short for 107 modulo 3 and it can also be called 107 modulus 3.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 107 mod 3?" you are asking "What is the Remainder when you divide 107 by 3?".
We will show you two methods of finding 107 mod 3 (107 modulo 3). 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 107 is the Dividend, 3 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 107 mod 3 using the Modulo Method, we first divide the Dividend (107) by the Divisor (3).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (3).
Then finally, we subtract the answer in the second step from the Dividend (107) to get the answer. Here is the math to illustrate how to get 107 mod 3 using our Modulo Method:
107 ÷ 3 ≈ 35.666667
35 × 3 = 105
107 - 105 = 2
Thus, the answer to "What is 107 mod 3?" is 2.
Modulus Method
To find 107 mod 3 using the Modulus Method, we first find the highest multiple of the Divisor (3) that is equal to or less than the Dividend (107).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 107 modulus 3 (107 mod 3):
Multiples of 3 are 0, 3, 6, 9, etc. and the highest multiple of 3 equal to or less than 107 is 105. Therefore, to get the answer:
107 - 105 = 2
Thus, once again, the answer to "What is 107 mod 3?" is 2.
Modulo Calculator
Do you have another "mod" problem you need solved? If so, please enter it here.