Tool to list multiples of a number. A multiple of a number is another number calculated with the product of this number by an integer.
Multiples of a Number - dCode
Tag(s) : Arithmetics, Series
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Multiples of a Number
Calculate multiples of a number N
Multiple Checker (Is it a multiple of N?)
Calculus of common multiples to 2 numbers
Answers to Questions (FAQ)
What is a multiple? (Definition)
A multiple of a number $ n $ is another number calculated by multiplying $ n $ by an integer (relative).
Example: $ 6 $ is a multiple of $ 2 $ because $ 2 $ multiplied by $ 3 $ equals $ 6 $
Example: $ k \times x $ is a multiple de $ x $ (with $ k \in \mathbb{Z} $)
How to list multiples of a number?
To list multiples of a number, take a number and multiply it by a quantity/factor/coefficient (2, 3, 4 etc.) to get a multiple.
It exists an infinite number of multiples, so it is impossible to list all multiples of a given number, dCode suggest to fix an upper and lower bound (all multiples between A and B).
Example: $ N = 3 $, so $ N \times 2 = 6 $, $ 6 $ is a multiple of $ 3 $,
$ N \times 3 = 9 $, $ 9 $ is a multiple of $ 3 $, etc.
| Multiples of 1 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, … |
| Multiples of 2 | 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, … |
| Multiples of 3 | 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, … |
| Multiples of 4 | 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, … |
| Multiples of 5 | 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, … |
| Multiples of 6 | 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, … |
| Multiples of 7 | 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, … |
| Multiples of 8 | 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, … |
| Multiples of 9 | 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, … |
| Multiples of 10 | 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, … |
| Multiples of 11 | 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, … |
| Multiples of 12 | 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, … |
| Multiples of 13 | 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, … |
| Multiples of 14 | 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, … |
| Multiples of 15 | 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, … |
For school multiplications, use a calculator here (affiliate link)
How to find if a number A is a multiple of B?
Divide A by B,if the result is an integer (the remainder of Euclidean division is 0), then A is a multiple of B, and B is a divisor of A.
Example: Is 60 a multiple of 4? Divide 60 by 4, 60/4 = 15 (integer without decimals after the decimal point), remain 0, so 60 is a multiple of 4 and 4 is a divisor of 60.
Example: Is 22 a multiple of 4? Divide 22 by 4, 22/4 = 5.5 (non-integer number, with decimals after decimal point) ie 22/4 = 5 + remainder 2, so 22 is not a multiple of 4 and 4 is not a divisor of 22.
How to find common multiples between two integer numbers?
To find common multiples between two integers, list the multiples of each number separately, then identify the numbers that appear in the lists of multiples of each.
dCode has a tool to calculate the LCM (least common multiple) of two numbers. Other multiples are multiples of the given LCM.
Example: The LCM for $ 3 $ and $ 8 $ is $ 24 $, the multiples common to $ 3 $ and $ 8 $ are all the multiples of $ 24 $ : $ 24, 48, 72, 96, … $
Is zero 0 a multiple?
Yes, in theory, 0 is multiple of all numbers because whatever $ n $, $ 0 / n = 0 $. In practice, it is often omitted from the list of multiples.
Zero is a multiple of every integer (except itself)
Are all numbers multiple of 1?
Yes, all numbers are multiples of 1 (and -1), but it is wrong to say that 1 is a multiple of all numbers, but it is true to say that 1 is a divisor of all numbers.
What is the difference between a multiple and a divisor?
A multiple is a multiplication result, it is a number obtained by multiplying another number by an integer. A divisor, on the other hand, is a number by which another number can be divided without leaving a remainder. Divisors are also called factors.
Are there negative multiples?
Yes, multiples can be negative, but they are usually omitted because they are the same as positive multiples, by a factor of -1, so with a -(minus) in front.
What is the algorithm for generating the list of multiples of a number?
The list is infinite, but assuming a limit in number of multiples, here is a source code: // Pseudo-code
function generateMultiples(n) {
multiples = []
limit = 1000
for i from 1 to limit {
multiple = n * i
multiples []= multiple
}
return multiples
}
Source code
dCode retains ownership of the "Multiples of a Number" source code. Except explicit open source licence (indicated Creative Commons / free), the "Multiples of a Number" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Multiples of a Number" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Multiples of a Number" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.
Cite dCode
The copy-paste of the page "Multiples of a Number" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Multiples of a Number on dCode.fr [online website], retrieved on 2024-11-21,
- Calculate multiples of a number N
- Multiple Checker (Is it a multiple of N?)
- Calculus of common multiples to 2 numbers
- What is a multiple? (Definition)
- How to list multiples of a number?
- How to find if a number A is a multiple of B?
- How to find common multiples between two integer numbers?
- Is zero 0 a multiple?
- Are all numbers multiple of 1?
- What is the difference between a multiple and a divisor?
- Are there negative multiples?
- What is the algorithm for generating the list of multiples of a number?
