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Prime factor decomposition


Any natural number greater than 1 can be decomposed into a product of two or more factors.

Number 24 decomposition in a product:
24 = 4x6
24 = 2x2x6
24 = 2 x 2 x 2 x 3 = 23 x 3

In the 2x2x2x3 product, all factors are prime.

We call it factorization of 24 the decomposition of 24 into a prime factor product. So the factorization of 24 is 23 x 3.

Generally speaking, we call factorization of a natural number, bigger
that 1, its decomposition into a prime factor product.

Practical Rule for Factoring

There is one practical device to factor a number. Follow in the example the steps to mount this device:

1) We divide the number by its smallest prime divisor;

2) then we divide the quotient obtained by the smallest prime divisor of that quotient and so on until we get quotient 1.

The figure shows the factorization of the number 630.

So 630 = 2 x 3 x 3 x 5 x 7.
630 = 2x32 x 5 x 7.

Next: Determining the Dividers of a Number