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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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