Factoring of a number is the number decomposition into prime factors.

If we start from a **composite number**, by definition we can get your “**decomposition**” in factors less than the same number, these factors may, in turn, composite numbers or prime. If they are composites, We decompose in the same way in order to decomposition in a **prime factors **.

Example:

El **12** can be decomposed in **12 = 3 · 4**, and in turn **4 = 2 · 2** therefore **12 = 3 · 2 · 2**

El **12** can be decomposed too in **12 = 2 · 6**, and in turn **6 = 2 · 3** therefore **12 = 2 · 2 · 3**

2 ways to obtain factors of 40

whatever the factorization, in the end the prime factors are **the same **because there are ** unique** possible decomposition in prime numbers.

Knowing this property, the more comfortable procedure to factoring is to use always the **primes** to split and the quotient to decompose.

**¿HOW TO FACTORING?**

Check if the number is **divisible by 2**; if it is, we make the **Division** and test with the quotient again with 2; if it’s not divisible we will see if it’s **divisible by 3**; and will repeat the **same procedure** than before. This will be repeated until the **quotient it’s 1**.

**Factors of: 28, 70, 32 **y** 210**:

**FACTORING FOR CALCULATING G.C.D. and L.C.M.**

Factoring is also used to calculate the **greatest common divisor** (GCD) and **least common multiple** (LCM)

gcdof two numbers is the result of the common factors powered tosmallest exponent.

lcmof two numbers is the result of the common and not common factors powered tohighest exponent.

**Example:**

Calculate the **gcd** of **72** and **50**

**72** = **2**^{3} · **3**^{2}

**50**=**2 ·** **5**^{2}

**gcd(72,50) = 2**

Calculate the **lcm** of **72** and **50**

**lcm(72,50) = 2 ^{3} · 3^{2} · 5^{2} = 1800**

We can use factoring to find out if a number **is prime**, as this will be prime when factoring only has as its prime factors 1 and the same.