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0. Modulo Method First need to divide the Dividend by the Divisor: 2 4 = 0.50 Next we take the Whole part of the Quotient (0) and multiply that by the Divisor (4): 0 x 4 = 0. And finally, we take the answer in the second step and subtract it from the Dividend to get the answer to 2 mod 4: 2 - 0 = 2.
Definition. The Modulus is the remainder of the euclidean division of one number by another. % is called the modulo operation. For instance, 9 divided by 4 equals 2 but it remains 1. Here, 9 / 4 = 2 and 9 % 4 = 1. In your example: 5 divided by 7 gives 0 but it remains 5 (5 % 7 == 5). Calculation.
Although Java has a remainder operator for int and long types, it has no modulus function or operator. I.e., -12 % 10 = -2 whereas -12 mod 10 = 8. If % operator returns a negative value for n % m, then (n % m) + m will give you n mod m. BigInteger provides functions for both and the specifications for them explain the difference quite well.
Modulus is just the remainder in division before its used in a decimal quotient. Example: The division of two numbers is often expressed as a decimal number (quotient). But the result of the division of say, 1/3, can also be expressed in whole numbers as "0 with a remainder of 1". But that form of quotient is not very helpful in modern math, so ...
The cast to unsigned long long above allows modulus to be as large as 2 32 - 1, assuming unsigned int is 32 bits, without the computation overflowing. With this approach, I was able to very quickly find answers even for very large inputs. For example, 111111111 returns 667332. I verified 2 677332 mod 111111111 == 1 using the arbitrary precision ...
4. Answering your specific questions: mod is a remainder operator. If applied to a series of numbers x in 0, 1, ..., then x mod n will be 0, 1, ..., n-1, 0, 1, ..., n-1, ad infinitum. When your modulus n is a power of 2, then x mod n will count up in binary from 0 to n-1, back to 0, to n-1, etc; for modulus n that looks like binary 01xxxxx, x ...
In modular arithmetic, one defines classes of numbers based on the modulo. In other words, in modulo m arithmetic, a number n is equivalent (read: the same) to n + m, n - m, n + 2m, n - 2m, etc. One defines m "baskets" and every number falls in one (and only one) of them. Example: one can say "It's 4:30 pm" or one can say "It's 16:30".
89. MySQL, SQL Server, PostgreSQL, SQLite support using the percent sign as the modulus: WHERE column % 2 = 1. For Oracle, you have to use the MOD function: WHERE MOD(column, 2) = 1. edited Sep 21, 2010 at 2:56. answered Sep 21, 2010 at 2:51. OMG Ponies.
1. I don't think you completely understand modulus. The '%' symbol reads mod or modulus. Essentially 2 mod 3 = 0 with a remainder of 2. The remainder of 2 is your answer. 2 mod or % 3 = 2. edited Feb 20, 2017 at 23:00. answered Feb 20, 2017 at 22:59. Chris Cruz.
The identity you're looking for is x mod N = (x mod 2^q)- c*floor(x/2^q), given that N = 2^q + c and c is any integer (but typically ±1). You may want to read section 9.2.3: "Moduli of special form" in "Prime Numbers: A Computational Perspective" by Richard Crandall and Carl Pomerance.