Created by Browserling
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!
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.
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.
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.
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!
Quickly rewrite integer digits using pretty Unicode glyphs.
Quickly generate random two-dimensional integer points.
Quickly generate random three-dimensional integer points.
Quickly print a list of integers that are palindromes.
Quickly convert the given integer to a palindromic integer.
Quickly find all integers in the given text or string.
Quickly make integer digits go in a triangle wave.
Quickly unleash the destructive force of Zalgo on integers.
Quickly find two or more integers that add up to the given integer.
Quickly find several integers that multiply up to the given integer.
Quickly randomize the given sequence of integers.
Quickly mix the order of digits in an integer.
Quickly put integers in increasing or decreasing order.
Quickly sort the individual digits of an integer.
Quickly increase all integers by a certain amount.
Quickly increase individual digits by a certain amount.
Quickly decrease all integers by a certain amount.
Quickly decrease individual digits by a certain amount.
Quickly randomly select an integer from a list of integers.
Quickly create groups from the digits of an integer.
Quickly write integer digits backwards.
Quickly remove one or more digits from an integer.
Quickly replace one or more digits in an integer.
Quickly drop digits from an integer and make it shorter.
Quickly add the thousands separator to integers.
Quickly remove the thousands separator from integers.
Quickly find the largest integer in a list of integers.
Quickly find the smallest integer in a list of integers.
Quickly find the total sum of a bunch of integers.
Quickly find the sum of all the digits in an integer.
Quickly find the total product of a bunch of integers.
Quickly find the product of all the digits in an integer.
Quickly calculate the partial sum of a bunch of integers.
Quickly calculate the partial product of a bunch of integers.
Quickly flip the sign of one or more integers.
Quickly split an integer into chunks of a given length.
Quickly merge partial integers together to form a larger integer.
Quickly round integers up or down to the required precision.
Quickly convert integers to a downloadable picture.
Quickly generate a list of von Neumann ordinals.
Quickly generate a list of Zermelo ordinals.
Quickly generate an ordered sequence of integers.
Quickly generate an ordered list of even integers.
Quickly generate an ordered list of odd integers.
Quickly write an integer spelling in words.
Quickly convert spelled integers to regular integers with digits.
Quickly generate an array of integers for programming.
Quickly find the number of occurrences of digits in integers.
Create a drawing that visualizes von Neumann hierarchy of sets.
Create a sudoku puzzle.
Create a list of neat-looking integers (called magic integers).
Generate a list of tuples of integers with n elements.
Quickly convert integers to base one.
Quickly convert base one to integers.
Quickly convert integers to base two.
Quickly convert base two to integers.
Quickly convert integers to base eight.
Quickly convert base eight to integers.
Quickly convert integers to base sixteen.
Quickly convert base sixteen to integers.
Quickly encode integers to base-64.
Quickly decode base-64 to integers.
Quickly convert integers to a custom base.
Quickly encode integers to HTML encoding.
Quickly decode HTML entities to integers.
Quickly encode integers to URL (percent) encoding.
Quickly decode URL-encoded integers.
Quickly convert a signed integer to an unsigned integer.
Quickly convert an unsigned integer to a signed integer.
Generate a list of random integers.
Check if the given integers are palindromes.
Create a matrix whose entries are all integers.
Create a vector with integer coefficients.
Quickly calculate the average value of integers.
Quickly calculate the average value of integer digits.
Quickly randomly select a digit from an integer.
Find which of the given integers is the biggest or smallest.
Limit integer values to a range.
Limit integer digit values to a range.
Create multiple copies of the input integers.
Create multiple copies of digits of input integers.
Rotate the digits of an integer to the left or right.
Move the digits of an integer to the left or right.
Quickly find the difference of a bunch of integers.
Quickly apply the bitwise AND operation to integers.
Quickly apply the bitwise OR operation to integers.
Quickly apply the bitwise XOR operation to integers.
Quickly apply the bitwise NOT operation to integers.
Quickly apply the bitwise NAND operation to integers.
Quickly apply the bitwise NOR operation to integers.
Quickly apply the bitwise NXOR operation to integers.
Quickly divide two or more integers.
Quickly divide the digits of an integer.
Add -st, -nd, -rd, -th suffixes to integers to make them ordinals.
Remove -st, -nd, -rd, -th suffixes from ordinals to make them ints.
Find integers that match a filter (greater, less, equal).
Add padding to integers on the left side.
Add padding to integers on the right side.
Position all integers so that they align on the right.
Position all integers so that they align in the middle.
Turn all integers into positive integers.
Turn all integers into negative integers.
Rewrite an integer in fractional form.
Extract the numerator and denominator from a fraction.
Search for all occurrences of an integer and replace it.
Create a regex that matches the given integers.
Create integers that match the given regular expression.
Create relatively tiny integers.
Create relatively huge integers.
Create a sequence of oscillating integers, such as 123212321.
Create multiple integer sequences at once.
Slightly change an integer so it has an error.
Slightly change integer digits so there are errors.
Apply fuzzing to integers and add perturbations.
Apply fuzzing to integer digits and add digit perturbations.
Add highlighting to certain integers.
Add highlighting to certain integer digits.
Add color to integers based on a condition.
Add color to individual digits in the given integers.
Quickly assign colors to integers and draw them as pixels.
Quickly assign integer values to pixel colors and print them.
Make the digits of an integer go in a spiral shape.
Make the digits of an integer go in a circle.
Make the digits of an integer go in a diamond shape.
Fill a box with certain width and height with digits.
Use ASCII art to convert integers to 2-dimensional drawings.
Use ASCII art to convert integers to 3-dimensional drawings.
Decompose an integer into ones, tens, hundreds, etc.
Generate an ordered list of increasing integers.
Generate an ordered list of decreasing integers.
Quickly find various information about the given integers.
Find hidden patterns of numbers in integers.
Find the Shannon entropy of an integer.
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