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Learn what modulo is and how to use it in math and programming. Find examples, notation, and interactive activities on modulo and addition, multiplication, and digital roots.
Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. [1]
LanguageOperatorIntegerFloating-pointMODYesYes%YesNomodYesNoremYesNoIn mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.
An Introduction to Modular Math. When we divide two integers we will have an equation that looks like the following: A B = Q remainder R. A is the dividend. B is the divisor. Q is the quotient. R is the remainder. Sometimes, we are only interested in what the remainder is when we divide A by B .
- It is true that 5 divided by 3 gives you a remainder of 2 However, it is NOT true that -5 divided by 3 gives you a remainder of 2. It gives you a r...
- Johann Carl Friedrich Gauss is usually attributed with the invention/discovery of modular arithmetic. In 1796 he did some work that advanced the fi...
- Yes, it works. It's a cool discovery, but you weren't the first one to discover it. Here's a simple explanation of how it works. For our mod n circ...
- The modulus must be a positive integer i.e. an integer > = 1
- You said -7 *2 = -14, but -14 is actually bigger than -17. We have to go a little further. The next step would be -7*3 = -21, which is smaller than...
- 3 / 10 = 0 with a remainder of 3 3 mod 10 gives us the remainder when we divide 3 by 10. Thus 3 mod 10 = 3
- 13 mod 10. 1 R 3 10/13 10 3 The remainder is 3. 13 mod 10 is 3. I think this method of modulus is easier than the modulus method. What do you think?
- You are correct when you say if we have A ≡ B (mod C) then this will mean when A or B is divided by C the remainder will be the same For more info,...
- Indeed, 5 is a positive number, and -5 is a negative number. However, for the example: "-5 mod 3 = ? With a modulus of 3 we we make a clock with nu...
Definition: Modulo. Let \(m\) \(\in\) \(\mathbb{Z_+}\). \(a\) is congruent to \(b\) modulo \(m\) denoted as \( a \equiv b (mod \, n) \), if \(a\) and \(b\) have the remainder when they are divided by \(n\), for \(a, b \in \mathbb{Z}\).
The modulo (or "modulus" or "mod") is the remainder after dividing one number by another. Example: 100 mod 9 equals 1 Because 100/9 = 11 with a remainder of 1
In mathematics, the term modulo ("with respect to a modulus of", the Latin ablative of modulus which itself means "a small measure") is often used to assert that two distinct mathematical objects can be regarded as equivalent—if their difference is accounted for by an additional factor.
