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# 21 mod 3

Welcome to 21 mod 3, our post which explains the mathematical operation 21 modulus 3.

This is also known as remainder of 21 divided by 3, and if you have been looking for 21 modulo 3, then you are right here, too.

Read on to find the 21 mod 3 value as well as the math in a nutshell.

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## 21 Modulo 3

21 modulus 3 stands for the Euclidean division discussed, defined and explained in full detail on our home page.

The result of this modulo operation is:

21 mod 3 = 0

21 is the dividend, 3 is the divisor (modulo), 7 is the quotient explained below, and 0 is called the remainder.

The division rest of 21 by 3 equals 0, and the value of the quotient is 7.

Proof: 21 = (3×7) + 0.

Note that there is no other quotient q than 7, and that there is no other remainder r than 0 which solves the equation 21 = (3×q) + r and 0 ≤ r < 3; r ∈ set of real numbers R; q ∈ set of whole numbers Z.

Now that you understand what 21 mod 3 means, it’s time to zoom in on how this modulo operation is actually calculated.

Step by step, easy and straight to the point.

You can find the math the next part of this post.

## How is 21 mod 3 Calculated?

To obtain 21mod3 conduct these three steps:

1. Integer division (result without fractional part) of dividend by modulus: 21 / 3 = 7
2. Multiplication of the result right above (7) by the divisor (3): 7 × 3 = 21
3. Subtraction of the result right above (21) from the dividend (21): 21 – 21 = 0.

Calculation examples similar to the modulo division 21%3, but more detailed, can be found in our article in the header menu.

There you can also locate additional information about the Euclidean division.

Other operations belonging to the modulo 3 division category include, for example:

Note that you can locate all of our calculations, including 21 modulus 3, quickly, by filling in the search box placed in the header and sidebar; the result page contains all relevant posts.

Ahead is the summary of our information.

## Remainder of 21 Divided by 3

You have reached the final section of this post, and you should be able to answer questions like what is 21 mod 3?, compute is value, and name its part.

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