Once you know the basics of math, like how to add, subtract, divide, and multiply, you start using it in your everyday life without even realising it. The alphabets are the same way. When you talk, you look for a better word to add to your vocabulary, but the alphabets don’t change. Factoring is another one of those math ideas that seems hard at first, but once you start doing it and get better at it, you won’t even realise how often you use it.

Today, we’re going to talk about the factors of 6 and how to find them and tell if they are prime factors or not.

## Getting the Factors of 6

Before we can move on and figure out how to find the factors of 6, we need to understand what factors are and how they are different from multiplication and division.

When you multiply two or more whole numbers together, you get the product. All of the tables for multiplying that you see in math books come from finding the factors.

Now that we know what a factor is, we can move on to the next step, which is to find the factors of 6. When you look at its properties, the number 6 is quite important. It is the smallest positive integer that is neither a square nor a prime number. Also, 6 is the perfect number with the fewest digits.

When you multiply two whole numbers, you don’t have to go to great lengths to get the number 6 as a product. Here is a list of all the things that make up 6.

The only elements of 6 are 1 and 2, 3 and 6. None of the other numbers are considered to be factors of 6. Let’s talk about why this is the case.

Given Number | Multiples of given number/ Multiplicaltion Table |

1 | 1,2,3,4,5,6,… |

2 | 2,4,6,8,10,12,… |

3 | 3,6,9,12,15,18,… |

6 | 6,12,18,24,30,36,… |

Here, you can see that 6 has come up in the multiples of 1, 2, 3, and 6. But if you look at the table below, you can see what happens when you multiply 4 and 5. You will see that there is no 6 in multiples, even though the numbers are less than 6. So, 6 4, and 5 can’t be on our list of factors of 6.

4 | 4,8,12,16,20,24,… |

5 | 5,10,15,20,25,30,… |

Note: Keep in mind that the factors of a given number can’t be bigger than that number. For example, if you want to find the factors of 10, you only need to go from 1 to 10. Once you get to 10, you’ve reached the top, and when you multiply whole numbers from that point on, you won’t get 10.

## The prime factors of 6

Now that we know the factors of 6, let’s see what else we can find in these four numbers. You may have heard of prime numbers, which are numbers that can only be divided by themselves and 1. So let’s try to figure out 6’s prime factors and the factors it shares with 8.

2, 3 are prime numbers

When multiplying 2*3, we get 6.

So, only 2 and 3 are prime numbers among the given list of factors. When you try to solve the prime factorization of 6, it looks like this.

Find the factors of the expression 8 = 1, 2, 4, and 8.

1 and 2 are in both the 6 and 8 factors. So, 1,2 is the only thing that both 6 and 8 have in common.

## Examples That Worked

Now that we know what the factors are, we’ll work through an example that shows all six factors.

First, find two numbers that add up to 6 when added together. It’s easy, two, and three.

So 2X3 = 6.

Find the numbers that, when multiplied, add up to 2 and 3.

2 = 2X1

3 = 3X1

From this, we learned that 2 and 3 are factors, along with 1. The last two factors of 6 are and.

1, 2, 3, and 6.

We’ve shown you how to find a number’s factors and its common factors, and now we’d like you to figure out how to answer some questions on your own.

## Need to Break Down

Why do teachers start teaching factorization to kids so young? Why is it important to break a number down into its parts? All these questions arise in our minds. In math, adding, subtracting, multiplying, and dividing are just as important as factors and multiples. Factors and multiples are also taught to students as early as the fourth grade. Getting rid of factors and multiples of a number is an important topic to learn as early as the third grade. The points below show why factorization is important:

- Using factoring to solve problems with numbers is helpful.
- Large numbers are hard to figure out, so they are broken up into factors to make things easier.
- Taking the factors of a number is important because it helps solve equations with big numbers.

## Factors and Multiples: How They Work Together

In math, students also learn about multiples and factors in addition to how to add, subtract, and multiply. Factors and multiples are related to one another. A number can have just one factor or more than one. Every number is a multiple of itself and a factor of the product of two multiples. Because of this, both multiples and factors are linked.

In order to solve quadratic and linear equations, the factors of a number are used.

They are very useful for many math ideas.

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### Information about factors

1. Every number contains one as a component. Additionally, it is the least crucial.

**example** 1 × 25 = 25, 1 × 676 =676

2. The number itself is the most important thing about it.

**For example**, 281 =28 is the greatest factor of 28.

3. A number’s factor is always less than or the same as the number itself.

**For example**, 1, 2, 3, 4, 6, and 12 are all factors of the number 12.

1<12, 2<12, 3<12 ….. and 12 = 12.

4. Since it is not possible to divide by zero, zero is not a factor of any number.

An even number can be broken down into both even and odd parts, but an odd number can only be broken down into odd parts.

**For example**, the factors of 10 are 1, 2, 5, and 10 (both even and odd numbers count as factors). The factors of 9 are 1, 3, and 9. (only odd numbers as factors).

5. A number has only a certain number of factors.

6. A factor exactly divides the number, leaving no extra space.

Numbers that divide the original number evenly or exactly are called “factors.” A factor is a whole number that can be used to divide a larger number without leaving any extra numbers.

A fraction can never be a factor. Some numbers only have two factors, which are 1 and the number itself. Other numbers, however, have more than two factors.

## Conclusion

This is all about factors and how to find them for a given number. Figure out how to find the factors of 6 and how they differ from the multiples. Focus on how factors are found so you can easily figure out what factors other numbers have.