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2 Factors Decomposition

Tool to decompose a number in 2 factors, this decomposition consists in finding 2 divisors which can be multiplied to give N.

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2 Factors Decomposition -

Tag(s) : Arithmetics

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# 2 Factors Decomposition

## Prime Factorization

### What is the two integer factorization? (Definition)

Any number $N$ has divisors, at least 2 ($1$ and $N$ are the divisors of all numbers) if the number $N$ is prime, but often much more when $N$ is composed ($N$ is not prime).

It is therefore always possible to factor a number into 2 integers, and there are often several possible ways.

Example: $6 = 1 \times 6 = 2 \times 3 = 3 \times 2 = 6 \times 1$

### How to find two factors of a numbers?

Perform a search of all the divisors of the number N. All the combinations of 2 factors having for product the number N are the pairs $d_1, d_2$ with $d_1$ a divisor and $d_2 = N / d_1$ the result of the division.

Example: 12 can be decomposed into prime factors as 2*2*3. The list of divisors of 12 is therefore composed of 2, 3 but also 2*2=4 and 2*3=6. So couples of two factors can be deducted: 2*6 and 3*4 (There are also 12*1 but it is obvious).

Note that N is a multiple of all divisor numbers found.

The list obtained is exhaustive, but if there are many factors, the program could be limited to the first results.

### Why to find two factors of a numbers?

Factoring in 2 integers allows us to solve $a$ and $b$ in the equation $N = a \times b$. That is to say to find 2 divisors of $N$.

Example: From an area of a rectangle, the factorization makes it possible to find the height and the length.

### How to list divisors of a number?

Use the dCode tool for listing the divisors of any number.

### How to make a prime factor decomposition?

Use the dCode tool for prime factors decomposition.

## Source code

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