Here we will explain what 3 mod 15 means and show how to calculate it. 3 mod 15 is short for 3 modulo 15 and it can also be called 3 modulus 15.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 3 mod 15?" you are asking "What is the Remainder when you divide 3 by 15?".
We will show you two methods of finding 3 mod 15 (3 modulo 15). 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 3 is the Dividend, 15 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 3 mod 15 using the Modulo Method, we first divide the Dividend (3) by the Divisor (15).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (15).
Then finally, we subtract the answer in the second step from the Dividend (3) to get the answer. Here is the math to illustrate how to get 3 mod 15 using our Modulo Method:
3 ÷ 15 = 0.2
0 × 15 = 0
3 - 0 = 3
Thus, the answer to "What is 3 mod 15?" is 3.
Modulus Method
To find 3 mod 15 using the Modulus Method, we first find the highest multiple of the Divisor (15) that is equal to or less than the Dividend (3).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 3 modulus 15 (3 mod 15):
Multiples of 15 are 0, 15, 30, 45, etc. and the highest multiple of 15 equal to or less than 3 is 0. Therefore, to get the answer:
3 - 0 = 3
Thus, once again, the answer to "What is 3 mod 15?" is 3.
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