world's simplest integer tool

This browser-based utility rewrites an integer as a sum of several smaller integers and prints the additive decomposition in the output. You can specify the number of addends in the sum and the number of sums in the options. You can also change the order of the terms, customize the plus sign symbol, and the sum separator and surrounding characters. Created by math nerds from team Browserling.

With this online application, you can express an integer as a sum of two or more other positive values. For example, the integer 10 can be written using two terms as 4 + 6, using three terms as 5 + 3 + 2, using four terms as 1 + 4 + 2 + 3, or more terms. The decomposition 4 + 6 is considered to be the same as 6 + 4 because addition is commutative. You can specify the number of addends that need to go in the sum, as well as choose if the integer 0 should be used as an addend. If the zero addend is disabled, then the integer n can be decomposed into a sum that has strictly from 1 to n addends (in case of n addends, they are all 1's). If you allow the use of the zero, then it can consist of any number of addends as you can add as many zeros to an integer as you want and it won't change its value. The larger the input integer, the more integer partitions there are. For example, the integer 12 can be rewritten as a sum of 3 summands in 19 different ways and the integer 120 can be represented as 1238 unique sums. To make sure you get quick results and the output isn't too long, we have limited the output to 100 sums. You can increase or decrease this count in the options. By default, the summands are displayed from the smallest to the largest (for example, 1 + 1 + 2 + 8) but you can change their order in the options and print them from the largest to the smallest (for example, 8 + 2 + 1 + 1) or even in random order (for example, 1 + 8 + 2 + 1). You can also change the "+" sign to any other symbol, print the sums one after another (and not in a column), separate them with custom symbols, and also surround the sums with custom open and close symbols so that the output could immediately be used in Python or JavaScript programming languages. For example, if the open and close symbols are "(" and ")", and the summands are separated by commas, you will get tuples such as "(1, 1, 2, 8)". Integerabulous!

Click to try

In this example, we expand the integer 9 into a sum of three other integers, including the zero integer. It turns out that for this input integer there are twelve unique three-term sums. We print them one per line and display the summands in increasing order and place the regular plus symbol "+" between them.

9

0 + 0 + 9
0 + 1 + 8
0 + 2 + 7
0 + 3 + 6
0 + 4 + 5
1 + 1 + 7
1 + 2 + 6
1 + 3 + 5
1 + 4 + 4
2 + 2 + 5
2 + 3 + 4
3 + 3 + 3

Rewrite an integer as a sum of

this many smaller integers.

this many smaller integers.

Output this many different sums.

Allow "0" as an addend

in integer sums.

in integer sums.

Enter a custom plus symbol here.

Separate sums by this char.

Sum open symbol.

Sum close symbol.

Print integer addends from

small to large.

small to large.

In this example, we disallow the use of zero-summand and generate all possible commutatively-unique sum combinations of the integer 12. Without using a zero, the number of partitions is 11, while using a zero, it would have reached 58. We replace the plus sign with the colon character and output all terms in decreasing order. We make the output comma-separated that prints all sums on the same line and enclose each sum in a pair of curly brackets.

12

{7:1:1:1:1:1}, {6:2:1:1:1:1}, {5:3:1:1:1:1}, {4:4:1:1:1:1}, {5:2:2:1:1:1}, {4:3:2:1:1:1}, {3:3:3:1:1:1}, {4:2:2:2:1:1}, {3:3:2:2:1:1}, {3:2:2:2:2:1}, {2:2:2:2:2:2}

Rewrite an integer as a sum of

this many smaller integers.

this many smaller integers.

Output this many different sums.

Allow "0" as an addend

in integer sums.

in integer sums.

Enter a custom plus symbol here.

Separate sums by this char.

Sum open symbol.

Sum close symbol.

Print integer addends from

large to small.

large to small.

In this example, we split the integer 100 into random sums with eight addends. There are more than one million partitions for this input specification and it's too large to compute. To quickly get usable results, we have limited the output to just 15 values. They are printed in a vertical column as the sum separator symbol is set to "\n".

100

1+1+92+1+1+1+2+1
1+1+4+65+1+1+26+1
74+1+1+18+1+3+1+1
60+13+1+4+1+1+1+19
1+58+2+35+1+1+1+1
25+1+3+6+29+8+9+19
1+18+30+34+4+2+1+10
10+4+1+1+56+20+1+7
3+1+85+1+1+1+7+1
5+1+1+88+1+1+1+2
1+41+8+1+1+1+4+43
1+61+1+10+3+16+1+7
40+1+1+1+4+1+9+43
3+1+1+1+91+1+1+1
1+10+51+2+2+6+5+23

Rewrite an integer as a sum of

this many smaller integers.

this many smaller integers.

Output this many different sums.

Allow "0" as an addend

in integer sums.

in integer sums.

Enter a custom plus symbol here.

Separate sums by this char.

Sum open symbol.

Sum close symbol.

Print integer addends in

random order.

random order.

In this example, we enter a huge integer equal to nine billion and decompose it into sums of four terms. We limit the number of sums in the output to six, as there are nearly infinitely many of them and it would take a very long time to calculate them all. The sums are randomly generated each time when you click on the example and in each case, adding all the terms together produces 9,000,000,000.

9000000000

1711990448 + 1620447777 + 4513236069 + 1154325706
65092647 + 7195252690 + 1087127447 + 652527216
75025523 + 445960474 + 7275699612 + 1203314391
8859019917 + 27328377 + 36962265 + 76689441
3859074492 + 3054860384 + 1950209345 + 135855779
6999192102 + 502145916 + 975841729 + 522820253

Rewrite an integer as a sum of

this many smaller integers.

this many smaller integers.

Output this many different sums.

Allow "0" as an addend

in integer sums.

in integer sums.

Enter a custom plus symbol here.

Separate sums by this char.

Sum open symbol.

Sum close symbol.

Print integer addends in

random order.

random order.

In this example, the number of addends is greater than the input integer. In order to produce 8 terms that add up to the integer 6, some of the addends must be equal to 0. To allow this condition, we have enabled the "Include Zero" option, which creates two or more redundant zero terms in the sums. We print the sums in parentheses, separate terms by the comma character, and place zeros at the beginning of sums.

6

(0, 0, 0, 0, 0, 0, 0, 6)
(0, 0, 0, 0, 0, 0, 1, 5)
(0, 0, 0, 0, 0, 0, 2, 4)
(0, 0, 0, 0, 0, 0, 3, 3)
(0, 0, 0, 0, 0, 1, 1, 4)
(0, 0, 0, 0, 0, 1, 2, 3)
(0, 0, 0, 0, 0, 2, 2, 2)
(0, 0, 0, 0, 1, 1, 1, 3)
(0, 0, 0, 0, 1, 1, 2, 2)
(0, 0, 0, 1, 1, 1, 1, 2)
(0, 0, 1, 1, 1, 1, 1, 1)

Rewrite an integer as a sum of

this many smaller integers.

this many smaller integers.

Output this many different sums.

Allow "0" as an addend

in integer sums.

in integer sums.

Enter a custom plus symbol here.

Separate sums by this char.

Sum open symbol.

Sum close symbol.

Print integer addends from

small to large.

small to large.

You can pass input to this tool via __?input__ query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!

https://onlinetools.com/integer/rewrite-integer-as-sum__?input__=9&number-of-addends=3&number-of-sums=12&include-zero=true&plus-symbol=%20%252B%20&sum-separator=%255Cn&open-symbol=&close-symbol=&left-to-right=true

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Write Integers in a Fancy Font

Quickly rewrite integer digits using pretty Unicode glyphs.

Generate Integer Pairs

Quickly generate random two-dimensional integer points.

Generate Integer Triples

Quickly generate random three-dimensional integer points.

Generate Symmetric Integers

Quickly print a list of integers that are palindromes.

Palindromize an Integer

Quickly convert the given integer to a palindromic integer.

Extract Integers from Data

Quickly find all integers in the given text or string.

Create an Integer ZigZag

Quickly make integer digits go in a triangle wave.

Destroy Integers

Quickly unleash the destructive force of Zalgo on integers.

Rewrite an Integer as a Sum

Quickly find two or more integers that add up to the given integer.

Rewrite an Integer as a Product

Quickly find several integers that multiply up to the given integer.

Shuffle Integers

Quickly randomize the given sequence of integers.

Shuffle Integer Digits

Quickly mix the order of digits in an integer.

Sort Integers

Quickly put integers in increasing or decreasing order.

Sort Integer Digits

Quickly sort the individual digits of an integer.

Increment Integers

Quickly increase all integers by a certain amount.

Increment Integer Digits

Quickly increase individual digits by a certain amount.

Decrement Integers

Quickly decrease all integers by a certain amount.

Decrement Integer Digits

Quickly decrease individual digits by a certain amount.

Pick an Integer

Quickly randomly select an integer from a list of integers.

Separate Integer Digits

Quickly create groups from the digits of an integer.

Reverse Integer Digits

Quickly write integer digits backwards.

Delete Integer Digits

Quickly remove one or more digits from an integer.

Replace Integer Digits

Quickly replace one or more digits in an integer.

Truncate Integers

Quickly drop digits from an integer and make it shorter.

Add Commas to an Integer

Quickly add the thousands separator to integers.

Remove Commas from an Integer

Quickly remove the thousands separator from integers.

Find the Max Integer

Quickly find the largest integer in a list of integers.

Find the Min Integer

Quickly find the smallest integer in a list of integers.

Add Integers

Quickly find the total sum of a bunch of integers.

Add Integer Digits

Quickly find the sum of all the digits in an integer.

Multiply Integers

Quickly find the total product of a bunch of integers.

Multiply Integer Digits

Quickly find the product of all the digits in an integer.

Find the Running Total

Quickly calculate the partial sum of a bunch of integers.

Find the Running Product

Quickly calculate the partial product of a bunch of integers.

Change Integer Sign

Quickly flip the sign of one or more integers.

Split an Integer

Quickly split an integer into chunks of a given length.

Join Integers

Quickly merge partial integers together to form a larger integer.

Round Integers

Quickly round integers up or down to the required precision.

Create an Image from Integers

Quickly convert integers to a downloadable picture.

Generate von Neumann Ordinals

Quickly generate a list of von Neumann ordinals.

Generate Zermelo Ordinals

Quickly generate a list of Zermelo ordinals.

Enumerate Integers

Quickly generate an ordered sequence of integers.

Print Even Integers

Quickly generate an ordered list of even integers.

Print Odd Integers

Quickly generate an ordered list of odd integers.

Convert Integers to Words

Quickly write an integer spelling in words.

Convert Words to Integers

Quickly convert spelled integers to regular integers with digits.

Create an Integer Array

Quickly generate an array of integers for programming.

Analyze Integers

Quickly find the number of occurrences of digits in integers.

Created with love by

51K

@browserling

51K

@browserling

We're Browserling — a friendly and fun cross-browser testing company powered by alien technology. At Browserling our mission is to make people's lives easier, so we created this collection of integer tools. Our tools have the simplest user interface that doesn't require advanced computer skills and they are used by millions of people every month. Our integer tools are actually powered by our programming tools that we created over the last couple of years. Check them out!

These integer tools are on the way!

Draw von Neumann Universe

Create a drawing that visualizes von Neumann hierarchy of sets.

Generate a Sudoku Board

Create a sudoku puzzle.

Generate Magic Integers

Create a list of neat-looking integers (called magic integers).

Create Integer n-Tuples

Generate a list of tuples of integers with n elements.

Convert Integers to Unary Base

Quickly convert integers to base one.

Convert Unary Base to Integers

Quickly convert base one to integers.

Convert Integers to Binary Base

Quickly convert integers to base two.

Convert Binary Base to Integers

Quickly convert base two to integers.

Convert Integers to Octal Base

Quickly convert integers to base eight.

Convert Octal Base to Integers

Quickly convert base eight to integers.

Convert Integers to Hex Base

Quickly convert integers to base sixteen.

Convert Hex Base to Integers

Quickly convert base sixteen to integers.

Convert Integers to Base64

Quickly encode integers to base-64.

Convert Base64 to Integers

Quickly decode base-64 to integers.

Change Integer Base

Quickly convert integers to a custom base.

Convert Integers to HTML Entities

Quickly encode integers to HTML encoding.

Convert HTML Entities to Integers

Quickly decode HTML entities to integers.

Convert Integers to URL Encoding

Quickly encode integers to URL (percent) encoding.

Convert URL Encoding to Integers

Quickly decode URL-encoded integers.

Convert Signed Integer to Unsigned

Quickly convert a signed integer to an unsigned integer.

Convert Unsigned Integer to Signed

Quickly convert an unsigned integer to a signed integer.

Create Random Integers

Generate a list of random integers.

Check if an Integer is Symmetric

Check if the given integers are palindromes.

Generate an Integer Matrix

Create a matrix whose entries are all integers.

Generate an Integer Vector

Create a vector with integer coefficients.

Find Integer Average

Quickly calculate the average value of integers.

Find Integer Digit Average

Quickly calculate the average value of integer digits.

Pick an Integer Digit

Quickly randomly select a digit from an integer.

Compare Integers

Find which of the given integers is the biggest or smallest.

Clamp Integers

Limit integer values to a range.

Clamp Integer Digits

Limit integer digit values to a range.

Duplicate Integers

Create multiple copies of the input integers.

Duplicate Integer Digits

Create multiple copies of digits of input integers.

Rotate Integers

Rotate the digits of an integer to the left or right.

Shift Integer Digits

Move the digits of an integer to the left or right.

Subtract Integers

Quickly find the difference of a bunch of integers.

AND Integers

Quickly apply the bitwise AND operation to integers.

OR Integers

Quickly apply the bitwise OR operation to integers.

XOR Integers

Quickly apply the bitwise XOR operation to integers.

NOT Integers

Quickly apply the bitwise NOT operation to integers.

NAND Integers

Quickly apply the bitwise NAND operation to integers.

NOR Integers

Quickly apply the bitwise NOR operation to integers.

XNOR Integers

Quickly apply the bitwise NXOR operation to integers.

Divide Integers

Quickly divide two or more integers.

Divide Integer Digits

Quickly divide the digits of an integer.

Convert an Integer to Ordinal

Add -st, -nd, -rd, -th suffixes to integers to make them ordinals.

Convert an Oridinal to Integer

Remove -st, -nd, -rd, -th suffixes from ordinals to make them ints.

Filter Integers

Find integers that match a filter (greater, less, equal).

Left-pad Integers

Add padding to integers on the left side.

Right-pad Integers

Add padding to integers on the right side.

Right-align Integers

Position all integers so that they align on the right.

Center Integers

Position all integers so that they align in the middle.

Take Absolute Value of Integers

Turn all integers into positive integers.

Make All Integers Negative

Turn all integers into negative integers.

Convert Integers to Fractions

Rewrite an integer in fractional form.

Convert Fractions to Integers

Extract the numerator and denominator from a fraction.

Find and Replace Integers

Search for all occurrences of an integer and replace it.

Generate Regex from Integers

Create a regex that matches the given integers.

Generate Integers from a Regex

Create integers that match the given regular expression.

Generate Small Integers

Create relatively tiny integers.

Generate Big Integers

Create relatively huge integers.

Generate Oscillating Integers

Create a sequence of oscillating integers, such as 123212321.

Generate a Multi-integer Sequence

Create multiple integer sequences at once.

Introduce Errors in Integers

Slightly change an integer so it has an error.

Introduce Errors in Integer Digits

Slightly change integer digits so there are errors.

Make Integers Fuzzy

Apply fuzzing to integers and add perturbations.

Make Integers Digits Fuzzy

Apply fuzzing to integer digits and add digit perturbations.

Highlight Integers

Add highlighting to certain integers.

Highlight Integer Digits

Add highlighting to certain integer digits.

Color Integers

Add color to integers based on a condition.

Color Integer Digits

Add color to individual digits in the given integers.

Convert Integers to Pixels

Quickly assign colors to integers and draw them as pixels.

Convert Pixels to Integers

Quickly assign integer values to pixel colors and print them.

Draw an Integer Spiral

Make the digits of an integer go in a spiral shape.

Draw an Integer Circle

Make the digits of an integer go in a circle.

Draw an Integer Diamond

Make the digits of an integer go in a diamond shape.

Draw an Integer Box

Fill a box with certain width and height with digits.

Create 2D Integers

Use ASCII art to convert integers to 2-dimensional drawings.

Create 3D Integers

Use ASCII art to convert integers to 3-dimensional drawings.

Decompose an Integer

Decompose an integer into ones, tens, hundreds, etc.

Print Increasing Integers

Generate an ordered list of increasing integers.

Print Decreasing Integers

Generate an ordered list of decreasing integers.

Print Integer Information

Quickly find various information about the given integers.

Find Patterns in Integers

Find hidden patterns of numbers in integers.

Calculate Integer Entropy

Find the Shannon entropy of an integer.

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