Here we will explain what 110 mod 54 means and show how to calculate it. 110 mod 54 is short for 110 modulo 54 and it can also be called 110 modulus 54.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 110 mod 54?" you are asking "What is the Remainder when you divide 110 by 54?".
We will show you two methods of finding 110 mod 54 (110 modulo 54). 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 110 is the Dividend, 54 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 110 mod 54 using the Modulo Method, we first divide the Dividend (110) by the Divisor (54).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (54).
Then finally, we subtract the answer in the second step from the Dividend (110) to get the answer. Here is the math to illustrate how to get 110 mod 54 using our Modulo Method:
110 ÷ 54 ≈ 2.037037
2 × 54 = 108
110 - 108 = 2
Thus, the answer to "What is 110 mod 54?" is 2.
Modulus Method
To find 110 mod 54 using the Modulus Method, we first find the highest multiple of the Divisor (54) that is equal to or less than the Dividend (110).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 110 modulus 54 (110 mod 54):
Multiples of 54 are 0, 54, 108, 162, etc. and the highest multiple of 54 equal to or less than 110 is 108. Therefore, to get the answer:
110 - 108 = 2
Thus, once again, the answer to "What is 110 mod 54?" is 2.
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