The remainder in 1%3 refers to what remains of 1 (not 3) after you divide by 3. As you have already said, 3 goes into 1 zero times. So -- when you remove 0 multiples of 3 from 1, all of 1 remains. Thus 1 % 3 = 1.

Answer from John Coleman on Stack Overflow
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Omni Calculator
omnicalculator.com › math › modulo
Modulo Calculator
May 8, 2025 - A real-life example may be sharing a pizza with your friends or family. There are even uses for modulo in Minecraft. mod 64 will tell you how many full stacks of cobblestone you'll need to build that Creeper statue.
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I have the solution to this problem, but I don't understand the logic behind the solution.
First, tripling the range and then only considering the multiples of 3 is the same as using the original range and tripling each integer. The multiples of 3 will have all of their digits sum to a multiple of 3, as you mention. So, now we just want to know how many of the integers in the range consist of only odd digits, and whose digits sum to a multiple of 3. Next, you can consider mod results as negatives, but it isn’t actually necessary. 2 mod 3 = -1 mod 3. They used -1 so that it was (more) obvious that when you add it to 1 the result is 0. But 1 mod 3 plus 2 mod 3 is also 0. The only reason to use mods in this solution is to reduce the number of cases to consider. Rather than considering each possible odd digit at each location, using mods least you combine cases. The 0 mod 3 (odd) digits are 3 and 9. 1 mod 3 are 1 and 7. 2 mod 3 (or -1) is 5. The difference bullet points are just the different ways that the groups of digits can be combined to result in the digits summing to 0 mod 3. Then the counts are the size of that group (1 or 2), and they are multiplied together along with the number of permutations for that case. More on reddit.com
🌐 r/askmath
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October 22, 2023
Fast hardware implementation to calculate modulo 3? - repost

Whoa nelly.

Sorry about the deletion. I didn't think that the post was such a teaching moment.

No the original question was not for homework. I am out of school, despite what my questions may look like :) It actually came from a job interview I had just done and struggled with this as a question. The deletion came because I typically take notes in a text file locally, and pasted the reddit link in my notes to save. But when emailing the interviewer as a followup with notes, I pasted the reddit link in there as well in the body of the notes. I didn't want the interviewer to track down my post history using that link.

Anyway, sorry again. There was no ill intent in terms of "keeping information to myself". This repost should be fine as the original link doesn't point to it.

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🌐 r/FPGA
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November 6, 2018
Mod 3 worth it?
Pretty much up to you and your budget. I’m in it at 700 with holster 3 extra mags and a holosun. More on reddit.com
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November 24, 2024
XD Mod 3
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People also ask

How much is 17 mod 3?

17 mod 3 equals 2 since dividing 17 by 3 gives a quotient of 5 and a remainder of 2. The remainder is the result of the modulus operation. In simpler terms, 17 mod 3 = 2.

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omnicalculator.com
omnicalculator.com › math › modulo
Modulo Calculator
How to calculate modulo division?

To calculate modulo division: subtract the divisor from the dividend until the resultant is less than the divisor.

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omnicalculator.com
omnicalculator.com › math › modulo
Modulo Calculator
What is a modulo operator?

The modulo operator is used to find the remainder during a division of two numbers. The operator is represented by the symbol % in most programming languages. It is also known as the remainder operator. As an example, 5 mod 2 returns 1.

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omnicalculator.com
omnicalculator.com › math › modulo
Modulo Calculator
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Wikipedia
en.wikipedia.org › wiki › Modulo
Modulo - Wikipedia
3 weeks ago - For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0.
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Divisible Info
divisible.info › Modulo › What-is-1-mod-3.html
What is 1 mod 3? (1 modulo 3?)
Here is the math to illustrate how to get 1 mod 3 using our Modulo Method: 1 ÷ 3 ≈ 0.333333 0 × 3 = 0 1 - 0 = 1 Thus, the answer to "What is 1 mod 3?" is 1. Modulus Method To find 1 mod 3 using the Modulus Method, we first find the highest multiple of the Divisor (3) that is equal to or ...
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CalculatorSoup
calculatorsoup.com › calculators › math › modulo-calculator.php
Modulo Calculator
If you did not use the mod operator you would have to do the math in your code. For example you would have to calculate "is 496 a multiple of 4?". You would divide 496 by 4, so 496 / 4 = 124 with no remainder.
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BetterExplained
betterexplained.com › articles › fun-with-modular-arithmetic
Fun With Modular Arithmetic – BetterExplained
Give people numbers 0, 1, 2, and ... by 4 — whoever gets the remainder exactly goes first. (For example: if the sum of fingers is 11, whoever had “3” gets to go first, since 11 mod 4 = 3)....
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Cuemath
cuemath.com › questions › what-is-1-mod-3
What is 1 mod 3? [Solved]
To find 1 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, 1.
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Wikipedia
en.wikipedia.org › wiki › Modular_arithmetic
Modular arithmetic - Wikipedia
2 weeks ago - We say that 15 is congruent to 3 modulo 12, and we write 15 ≡ 3 (mod 12), so 7 + 8 ≡ 3 (mod 12). Similarly, if one waits 8 hours and then 8 more hours (thus 16 hours in total), the clock will show the same time change as if one waited 4 hours. This is reflected by the identity 2 × 8 ≡ 4 (mod 12). After a wait of exactly 12 hours, the hour hand will be right where it started, so 12 acts as 0; one writes 12 ≡ 0 (mod 12). Given an integer m ≥ 1, called a modulus, two integers a and b are said to be congruent modulo m, if their difference a − b is an integer multiple of m; that is, if there is an integer k such that
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Microsoft Learn
learn.microsoft.com › en-us › dotnet › visual-basic › language-reference › operators › mod-operator
Mod Operator - Visual Basic | Microsoft Learn
The following example uses the Mod operator to divide two numbers and return only the remainder. If either number is a floating-point number, the result is a floating-point number that represents the remainder. Debug.WriteLine(10 Mod 5) ' Output: 0 Debug.WriteLine(10 Mod 3) ' Output: 1 Debug.WriteLine(-10 Mod 3) ' Output: -1 Debug.WriteLine(12 Mod 4.3) ' Output: 3.4 Debug.WriteLine(12.6 Mod 5) ' Output: 2.6 Debug.WriteLine(47.9 Mod 9.35) ' Output: 1.15
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Calculators.org
calculators.org › math › modulo.php
Modulo Calculator
This diminishes the sum to a number ... N – 1. In his book, Gauss included a notation with the symbol ≡, which is read as “is congruent to.” Instead of the usual = symbol, the three horizontal line segments both signify equality and definition. For instance, if we add the sum of 2, 4, 3 and 7, the sum is congruent to 6 (mod 10). That’s 16 ≡ (mod 10). This means 16 divided by 10 leaves a remainder of 6. Likewise, 16 – 10 = 6. Another example, 13 ≡ 1 ...
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BYJUS
byjus.com › mod-calculator
How to Use the Mod Calculator?
May 4, 2020 - Hence, the 16 mod 3 is equal to 1. Another example of modulo function is 15 mod 3. In this case,15 is exactly divided by 3. Thus, the remainder should be 0.
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Divisible Info
divisible.info › Modulo › What-is-3-mod-1.html
What is 3 mod 1? (3 modulo 1?) - Divisible
Here is the math to illustrate how to get 3 mod 1 using our Modulo Method: 3 ÷ 1 = 3 3 × 1 = 3 3 - 3 = 0 Thus, the answer to "What is 3 mod 1?" is 0. Modulus Method To find 3 mod 1 using the Modulus Method, we first find the highest multiple of the Divisor (1) that is equal to or less than ...
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Reddit
reddit.com › r/askmath › i have the solution to this problem, but i don't understand the logic behind the solution.
r/askmath on Reddit: I have the solution to this problem, but I don't understand the logic behind the solution.
October 22, 2023 -

This is the problem, and this is the solution.

Already, on the first sentence I have a question. They just multiplied the end points of the range of integers the question asked us to consider by 3 and just said that would give us the same answer. I don't understand how those things are the same, nor do I understand why they multiplied by three specifically.

Then, they take the mod 3 of all the numbers the digits could be. They take 9 mod 3 and 3 mod 3. They get 0 for both, makes sense. 1 mod 3 and 7 mod 3 are 1, makes sense. But they take 5 mod 3 and get -1? What? Wouldn't it be 2? It is my understanding that mod is never negative.

Also, why take the mod 3 of the possible digits? How did that help? I assume it's somehow connected with the fact that a number divisible by 3 has the sum of its digits divisibly by three, but I don't see the connection.

Then, they use the modulus in a completely unclear way, at least to me. So, the first bullet point states that the amount of numbers that start with 3 followed by three digits that have a modulus of zero is the same as 2 * 2 * 2. I don't know how having the first digit be 3 followed by three numbers that divide evenly into 3 result in 23.

Similarly, the second bullet point states the amount of numbers that start with 3 and are followed by "one [0], one [1], and one [-1]" results in 3! * 2 * 2 * 1. I have no clue how they got that.

I have the same question for all the bullet points. How did the initial statement after the bullet point lead to the following statement after the dash.

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Rosalind
rosalind.info › glossary › modular-arithmetic
ROSALIND | Glossary | Modular arithmetic
$n$, the remainders are equal. For example, $14 \equiv 23 \mod 3$ because when we divide both 14 and 23 by 3, the remainder is 2 in both cases. Three fundamental facts in modular arithmetic are that if · $a \equiv b \mod n$ and · $c \equiv d \mod n$, then ·
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GeeksforGeeks
geeksforgeeks.org › engineering mathematics › modular-arithmetic
Modular Arithmetic | Engineering Mathematics - GeeksforGeeks
September 3, 2025 - The modular inverse of a mod m exists only if a and m are relatively prime i.e. gcd(a, m) = 1. Hence, for finding the inverse of a under modulo m, if (a x b) mod m = 1 then b is the Modular Inverse of a. Example: a = 5, m = 7 (5 x 3) % 7 = 1 hence, ...
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Microsoft Learn
learn.microsoft.com › en-us › office › vba › language › reference › user-interface-help › mod-operator
Mod operator | Microsoft Learn
If either number is a floating-point number, it is first rounded to an integer. Dim MyResult MyResult = 10 Mod 5 ' Returns 0. MyResult = 10 Mod 3 ' Returns 1. MyResult = 12 Mod 4.3 ' Returns 0.
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Reddit
reddit.com › r/fpga › fast hardware implementation to calculate modulo 3? - repost
r/FPGA on Reddit: Fast hardware implementation to calculate modulo 3? - repost
November 6, 2018 - So 1mod3 = 1, 2mod3 = 2, 3mod3 = 0. PROBLEM: Have a 64 bit value shifted in serially at a very high frequency. Upon the last bit [63] shifted in, compute a mod3 of all the bits with least number of clock cycles possible.
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Princeton University
web.math.princeton.edu › math_alive › Crypto › Lab2 › ModArithm.html
Math Alive Crypto 2
The number X (mod Y) is the remainder when X is divided by Y. (Remember X (mod Y) is pronounced X modulo Y.) For example: 7 modulo 3 is 1 because: 7 = 2 * 3 + 1 That is, when you divide 7 by 3, you get a remander of 1. The "modulo Y" terminology can also be used in the following way: Z = X ...