world's simplest integer tool

This browser-based utility rewrites an integer as a product of several integer factors and prints the multiplicative decomposition in the output. You can find all possible products or just a specific number of products. You can change the order of multipliers and exclude the trivial factor "1". You can also change the multiplication symbol and use a custom output format for the factors. Created by math nerds from team Browserling.

With this online application, you can disassemble an integer into a bunch of smaller integers that when multiplied together produce the original integer. This is done by finding all possible divisors of the given integer and then combining them in all possible ways so that their product equals the dividend. For example, if you enter the integer 20 as input data, the program will calculate its divisors, which are 1, 2, 4, 5, 10, 20. Then, it will combine and multiply these factors and find which ones create 20. These combinations are 1 × 20, 1 × 2 × 10, 1 × 4 × 5, 1 × 2 × 2 × 5. The multiplier "1" (also called the trivial multiplier) has no effect on the product as anything multiplied by one equals the same value. You can turn off the trivial multiplier in the options and avoid using "1". In this case, you'll get only three products: 2 × 10, 4 × 5, 2 × 2 × 5. If the input integer is an integer prime, for example, 7, then it has only two divisors, 1 and 7, and can be expressed in only one way as 1 × 7. According to the commutative property of multiplication, the product 1 × 7 is the same as 7 × 1, so we only print one result. If the trivial divisor option is turned off, then there are no results. You can change the order of the multipliers and sort them in increasing order, decreasing order, or random order. The number of multiplicative partitions depends on the number of divisors and how well they combine together. For example, for the integer 8192, there are 101 different products but for the integer 8193, there are only 2. To avoid unpredictably long calculations for large integers, we limit the number of products to 100, but you can increase or decrease this amount in the options. You can also customize the output format of products. For example, you can replace the default multiplying character "×" with "*", or "·", or any other. If you're doing programming, then you can also put the products in brackets, for example, {1 × 7}, (1 × 7), or [1 × 7], and change the separator between individual products. By default, it's the newline "\n", so all products form a vertical column and each product goes on a separate line, but you can use a comma or a semicolon. Integerabulous!

Click to try

In this example, we decompose the integer 100 into several products that use smaller integers. The value 100 is an even integer that has nine divisors including 1 and itself. These divisors are 1, 2, 4, 5, 10, 20, 25, 50, 100. From all these terms, the algorithm creates nine combinations that multiply up to the original value 100. We display each product on a new row, arranging the factors in ascending order, and using the Unicode "×" symbol as the multiplication character.

100

1 × 100
1 × 2 × 50
1 × 4 × 25
1 × 5 × 20
1 × 10 × 10
1 × 2 × 2 × 25
1 × 2 × 5 × 10
1 × 4 × 5 × 5
1 × 2 × 2 × 5 × 5

How many integer products

to find?

to find?

Allow using the trivial

factor "1" in integer

products?

factor "1" in integer

products?

Enter the symbol you want to

use as the multiplication symbol.

use as the multiplication symbol.

Insert this symbol between

products. (Newline by default).

products. (Newline by default).

Open product

character.

character.

Close product

character.

character.

Print the largest factor on

the right.

the right.

The input integer 20160 in this example, although not very large, has mighty powers. It has 84 divisors that can be combined into products to produce itself in 1260 ways (1261 ways including the trivial product 20160 × 1). Not to clutter the output with so many products, we limited the output length to just 50 products. We also disabled the option that uses the trivial divisor "1" and chose the display order to be descending (largest multipliers go first). To customize the output, we replaced the regular multiplication sign with the mid-line dot operator, put products in quoted square brackets, and separated them with the comma character.

20160

"[10080⋅2]", "[6720⋅3]", "[5040⋅4]", "[4032⋅5]", "[3360⋅6]", "[2880⋅7]", "[2520⋅8]", "[2240⋅9]", "[2016⋅10]", "[1680⋅12]", "[1440⋅14]", "[1344⋅15]", "[1260⋅16]", "[1120⋅18]", "[1008⋅20]", "[960⋅21]", "[840⋅24]", "[720⋅28]", "[672⋅30]", "[630⋅32]", "[576⋅35]", "[560⋅36]", "[504⋅40]", "[480⋅42]", "[448⋅45]", "[420⋅48]", "[360⋅56]", "[336⋅60]", "[320⋅63]", "[315⋅64]", "[288⋅70]", "[280⋅72]", "[252⋅80]", "[240⋅84]", "[224⋅90]", "[210⋅96]", "[192⋅105]", "[180⋅112]", "[168⋅120]", "[160⋅126]", "[144⋅140]", "[5040⋅2⋅2]", "[3360⋅3⋅2]", "[2520⋅4⋅2]", "[2016⋅5⋅2]", "[1680⋅6⋅2]", "[1440⋅7⋅2]", "[1260⋅8⋅2]", "[1120⋅9⋅2]", "[1008⋅10⋅2]"

How many integer products

to find?

to find?

Allow using the trivial

factor "1" in integer

products?

factor "1" in integer

products?

Enter the symbol you want to

use as the multiplication symbol.

use as the multiplication symbol.

Insert this symbol between

products. (Newline by default).

products. (Newline by default).

Open product

character.

character.

Close product

character.

character.

Print the largest factor on

the left.

the left.

This example rewrites integer 608 as a product in twelve ways (there are 19 ways in total). It mixes the order of multipliers in products and includes the factor "1" in expressions. It uses the asterisk character as the multiplication symbol and the parentheses "(" and ")" as open and close product symbols. One integer product is printed per line and the factors are shuffled in a different order each time you click on the example.

608

(608 ∗ 1)
(19 ∗ 32 ∗ 1)
(16 ∗ 1 ∗ 38)
(2 ∗ 1 ∗ 304)
(1 ∗ 152 ∗ 4)
(76 ∗ 8 ∗ 1)
(16 ∗ 19 ∗ 1 ∗ 2)
(1 ∗ 2 ∗ 76 ∗ 4)
(1 ∗ 2 ∗ 38 ∗ 8)
(2 ∗ 1 ∗ 2 ∗ 152)
(19 ∗ 8 ∗ 4 ∗ 1)
(38 ∗ 1 ∗ 4 ∗ 4)
(2 ∗ 4 ∗ 4 ∗ 1 ∗ 19)

How many integer products

to find?

to find?

Allow using the trivial

factor "1" in integer

products?

factor "1" in integer

products?

Enter the symbol you want to

use as the multiplication symbol.

use as the multiplication symbol.

Insert this symbol between

products. (Newline by default).

products. (Newline by default).

Open product

character.

character.

Close product

character.

character.

Print integer factors in

mixed order.

mixed order.

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-product__?input__=100&number-of-products=9&include-one=true&multiply-symbol=%20%25C3%2597%20&product-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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