Factors of 6

The thing with maths is once you understand the basics of it, like addition, subtraction, division, and multiplication, you start using it in your daily life without even noticing. It’s the same thing with the alphabets when you speak, you look for a better word to increase your vocabulary, but the alphabets remain the same. Factoring is another one of those maths concepts which looks a bit difficult at the starting, but when you start solving it and get better at it, you won’t even notice using it in your daily life. 

Today we are going to talk about factors of 6 and how you can find different factors of 6 and distinguish if they are prime factors or not? 

Method to Find Factors of 6

Before we move forward and start churning out the steps to know the factors of 6, we first need to know about factors, what they are, and how they are different from multiplication and division. 

Factors are the whole numbers which, when multiplied with one another give us the product. All the multiplication tables you see in maths books are the result of finding the factors. 

Once we are clear with the definition of factors, now let’s move to the next step which is finding the factors of 6. 6 in itself is quite important if you look at its properties, it is the smallest positive integer which is neither a square nor comes in your list of prime numbers. In addition to this, 6 is also the smallest perfect number. 

6 is not a big number, so to get it in the form of a product when multiplying two whole numbers, you don’t need to go to long lengths. Given below is the list of factors of 6.

1, 2, 3, and 6, yes, only these four numbers are factors of 6, all the other numbers are not considered to be factors of 6, let us explain to you why it is so. 

Here, you can see in the multiples of 1, 2, 3, and 6, we have come across 6. But if you look at the table given below which shows the multiplication of 4 and 5. You will see even though numbers are smaller than 6 still there’s no 6 in multiples. Thus, we can’t include 6  4 and 5 in our list of factors of 6. 

Note:- Keep this in mind factors of a given number cannot exceed itself, meaning, if you are trying to find the factors of 10, you only need to go through 1 to 10, that’s all, once you hit the 10, you’ve reached the upper limit, and from there 10 won’t come as a product when you multiply whole numbers. 

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Prime Factorization of 6

Now we have the factors of 6, let’s see what else we can find in these 4 numbers, you might have heard about prime numbers that are only divisible by themselves and the number 1. So let’s try to find out the prime factorization of 6, and its common factors with 8. 

2, 3 are prime numbers

When multiplying 2*3, we get 6.

Thus, from the given list of factors, we have only 2 and 3 that are prime numbers. This is what the prime factorization of 6 looks like when you try to solve it. 

Now, find the factors of 8 = 1, 2, 4, and 8.

1 and 2 are common in both factors of 6 and 8. Thus 1,2 are your common factors of given numbers 6 and 8.

Solved Examples 

Now, we know what the factors are, we are going to solve one example in which we are going to showcase all factors of 6. 

First, find two numbers whose product comes out to be 6. It’s simple, 2, and 3.

So 2X3 = 6.

Now find the numbers which can be multiplied to make a product 2 and 3. 

2 = 2X1

3 = 3X1 

From this, we found out 2 factors, 2 and 3, along with 1, so the final factors of 6 are.

1, 2, 3, and 6. 

We have given you a solved example of finding a factor of a given number along with its common factors, and now we would like you to solve some questions on your own. 

Need of Factorization 

Why is factorization taught at a very young age? Why are taking factors of a number important? All these questions arise in our minds. In maths, apart from factors and multiples, addition, subtraction multiplication, and division play a very vital role.  Students from class 4 itself also learn regarding factors and multiples at a very young age. Taking out factors and multiples of a number is an important chapter right from the third standard itself. The following points suggest why factorization is necessary:

• Factoring is useful in resolving various numbers-related problems.

• Large numbers are difficult to calculate hence they are broken into factors to simplify them.

• The importance of taking factors of a number resolves the issue of solving equations for large numbers.

Factors and Multiples-Their relation

In Mathematics along with addition, subtraction, and multiplication, students also learn about multiples and factors. The multiples and factors are interrelated. A number can have one or multiple factors. Every number is multiple of itself and a factor of the product of two multiples. Hence both multiples and factors are interrelated.

Factors of a number are taken for solving quadratic and linear equations.They go very handy for various maths concepts.

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Facts about factors

1. 1 is a factor of every number. It is also the smallest factor.

 example 1 × 25 = 25, 1 × 676 =676 

2. The greatest factor of a number is the number itself.

 For example, the greatest factor of 28 is 28 as 28× 1 =28 

3. A factor of a number is always smaller than or equal to the number.

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

1<12, 2<12, 3<12 ….. and 12 = 12.

4. As division by zero is not possible so zero is not a factor of any number.

An even number can have both odd and even numbers as factors but an odd number can have only odd numbers as factors.

For example, factors of 10 are 1, 2, 5, and 10 (both Even and Odd numbers as factors) factors of 9 are 1, 3, and 9 (only odd numbers as factors).

5. A number has finite/ Limited factors.

6. A factor divides the number exactly leaving no remainder.

Factors of a number are defined as numbers that divide the original number evenly or exactly. The meaning of a factor is a whole number that can divide a greater number without any remainder.

No factor can be a fraction. Some numbers will have only two factors, i.e. 1 and the number itself, whereas all some numbers will have more than two factors.

Conclusion

This is all about factors and how to find them for a particular number. Learn how to find the factors of 6 and their differences with the multiples. Concentrate on how factors are determined so that you can easily determine the factors of other numbers.