What is the Factor? Understand the Factor Easily for Kids to All Grades

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:

factor1

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 Highest common factor, also abbreviated as ‘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):
image
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):
image
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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