Here we will explain what 145 mod 3 means and show how to calculate it. 145 mod 3 is short for 145 modulo 3 and it can also be called 145 modulus 3.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 145 mod 3?" you are asking "What is the Remainder when you divide 145 by 3?".
We will show you two methods of finding 145 mod 3 (145 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 145 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 145 mod 3 using the Modulo Method, we first divide the Dividend (145) 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 (145) to get the answer. Here is the math to illustrate how to get 145 mod 3 using our Modulo Method:
145 ÷ 3 ≈ 48.333333
48 × 3 = 144
145 - 144 = 1
Thus, the answer to "What is 145 mod 3?" is 1.
Modulus Method
To find 145 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 (145).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 145 modulus 3 (145 mod 3):
Multiples of 3 are 0, 3, 6, 9, etc. and the highest multiple of 3 equal to or less than 145 is 144. Therefore, to get the answer:
145 - 144 = 1
Thus, once again, the answer to "What is 145 mod 3?" is 1.
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