**What Is a Factor?**

A factor **may be a** number **that you simply** multiply with another number to **arrive** at another number, typically **a factor** **is** 1 and the number itself. Like for number 2, factor 1 X 2, 1, **and a pair of** both are factors. **think about** a multiplication problem as factors being multiplied **to seek out** the **final number**. Similar way, 2 and 4 are factors of 8:

A number can have just two factors or can have **more than** two factors. But how? Let’s learn further.

Numbers With Only Two Factors

Let’s start by **viewing** numbers that have only two factors–for example, **the number** 2. How **does one** make 2 using multiplication? By multiplying 1 x 2 or 2 x 1. **we will** say that multiplying 2 and 1 **is that the** only **possibility to** make a product **of two**. And so, **we are able to** also say that 2 has only two factors: 1 **and number 2 itself**.

What about **the number** 3, **what do you think about** factors does 3 has? Let’s restate the question and ask: What numbers can we multiply together **to create** a product of 3? Well, **the sole** **thanks to** making 3 are by multiplying 1 x 3 or 3 x 1. So, **we will** say that 3 has only two factors: 1 **and three**.

One more example of **variety** with only two factors is 5. Why? Because **we are able to** only make 5 by multiplying 1 x 5 and 5 x 1. So, 5 only has two factors: 1 and 5.

Notice **that each one** three of the numbers we discussed above-had factors of 1 and itself.

• 5 had factors of itself (5) and 1

• 3 had factors of itself (3) and 1

• 2 had factors of itself (2) and 1

Numbers **like** 2, 3, 5,7 –and **the other** number that only has factors of itself and 1–are called prime numbers.

Numbers With **over** Two Factors

**Now that we’ve discussed numbers with only two factors, let’s take a glance at some numbers that have over two factors**.

Numbers that have **over** or more than two factors are called composite numbers.

Factors are numbers which **you’ll** multiply together **to reach **another number.

For Example, The numbers 2 **and no 5** are factors of 10 because 2 x 5 = 10.

A number can have many factors!

Example : 2 and 4 are factors of 8, because 4 x 2 = 8

Also, 1 **and no 8** **also can** be factors of 8, because 1 x 8 = 8

Therefore 1, 2, 4, 8 are all factors of 8

**Common Factor**

When **over** 2 factors are common between two or more numbers, then **this is often** **called** the ‘Common Factor’.

Let’s use an example **to grasp** this.

Let us find the common factors of 12 and 24

12 = 1, 2, 3, 4, 6, 12

24 = 1, 2, 3, 4, 6, 8, 12

After finding the factors for both numbers, **we all know** that the one’s common are 1, 2, 3, 4, 6, 12**Greatest common factor**

When you find all the factors of two or more numbers, **and a few** factors are common, then **the largest** **of these** common factors **is that the** * Greatest common factor*.

This is abbreviated as ‘GCF’.

**it’s**also

**called**

*, also abbreviated as ‘*

**Highest common factor****HCF’**.

Let’s use an example

**to understand the**HCF of the numbers 12 and 30.

First,

**we discover**the common factors

12 = 1, 2, 3, 4, 6

30 = 1, 2, 3, 6

After finding the common factors, we see that the numbers 6

**is that the**highest

**common factor**of 12 and 30.

Lowest

**common factor**

The lowest

**common factor**

**is the**lowest number

**that’s**common

**to 2**or more numbers.

If

**we glance**at

**the instance**

**used to**find

**the greatest**

**common factor**, we see that

**the lowest**

**common factor**for

**the no**12 and 30 are are 1.

**Multiplication and Factoring Using Areas**

Multiplying (x + 2) by (x + 3) **may be** represented like so (see Figure 1):

Figure 1

This makes **the subsequent** operations look rather simple:

(x + 2)( x + 3)

x 2 + 2x + 3x + 6

x2 + 5x + 6

Using **the area** method for multiplying binomials also makes factoring **a simple** task. **we are able to** visualize the squares and rectangles **in the shape of this** shape while thinking to ourselves, “Which two numbers have a sum of 5 (second term) and a product of 6 (third term)?” If **we glance** carefully, students have another method for understanding why we get the terms we do after multiplying the binomials shown. How does this relate to trinomials? **let’s examine**.

Multiplication and Factoring of Cubes

Let’s take the last example and multiply it by (x + 4). Like so (see Figure 2):

Figure 2

(x + 2)(x + 3)(x + 4)

(x2 + 5x + 6)(x + 4)

x3 + 9×2 + 26x + 24

Or geometrically (see Figure 2): This has awesome implications **for understanding** both the **surface areas** and volume of this figure. Since we already **worked out** the “face” of this cube earlier (x2+ 5x + 6), we’re basically multiplying that face by the length of x and by the length of 4. This yields:

x(x2 + 5x + 6) + 4(x2 + 5x + 6)

. . .

x3 + 9×2 + 26x + 24

Factoring The Cube

Once **we discover** the quadrinomial, the cube gives us an **indication** **of understanding** the lengths that created the quadrinomial. One would only **have to** **work out** which three numbers give us a sum of 9 (second term) and a product of 24 (last term). These numbers are 2, 3, and 4, so we’ll get (x + 2)(x + 3)(x + 4).

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