Rewrite Integer as Product - Multiplicative Decomposition Tool

What Is a Multiplicative Decomposition?

In mathematics, a multiplicative decomposition (or factoring) represents a positive integer $N$ as a product of positive integers. Unlike standard prime factorization (which only breaks a number down into its fundamental prime components, e.g. 12 = 2 x 2 x 3), multiplicative decomposition lists all possible groupings of factors. For example, the number 12 can be written as a product in several distinct ways:
12 = 12
12 = 2 x 6
12 = 3 x 4
12 = 2 x 2 x 3

Custom Constraints and Factor Calculations

Decompose integers systematically using our advanced configuration controls:

Exact Factor Count: Restrict results to combinations containing precisely $k$ elements. For example, finding all 3-factor combinations of 24.
Trivial Factor 1: Choose whether to include or exclude the trivial multiplier 1 in your factorizations (e.g. 24 = 1 x 24 or 24 = 1 x 2 x 12).
Distinct Factors Only: Filter out combinations containing repeated values. E.g. keeping 12 = 3 x 4, but removing 12 = 2 x 2 x 3.
Custom Multiplication Symbols: Format combinations using standard algebraic symbols: x, asterisk *, or middle dot ·.

Frequently Asked Questions

How are the factors ordered?

To avoid duplicate permutations (like 2 x 3 x 4 and 4 x 2 x 3) and keep the list clean, all factor combinations are systematically listed in non-decreasing order (where each factor is greater than or equal to the previous factor).

Why is the input limit set to 100,000?

Although the number of factor combinations grows much slower than addition partitions, checking all recursive combinations of huge numbers still consumes significant processing power. The limit ensures instant, lag-free calculations in your web browser.

How is this different from a Prime Factorization calculator?

A prime factorization calculator only yields the single set of prime numbers that multiply to the target. This tool yields all composite factor groupings (e.g. including composite factors like 4, 6, 8, etc.) along with the prime combinations.