See 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?
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.
See, factors are the whole numbers which, when multiplied with one another gives us the product. All the multiplication tables you see in maths books are the result of finding the factors, so now you know who to blame for the tables of 17, 18, and 19.
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 a form 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 then 6 still there’s no 6 in multiples. Thus, we can’t include 6 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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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.
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.
1. What are the rules for finding a factor?
As we have already told, factors are the numbers that you use to multiply from each other to find the other number. Some numbers that are present in mathematics have more than one way of factorization. There are some rules of factorization which will help you find the answer quickly.
First, the number for which you are looking to find a factor cannot have a bigger factor than the number given in the first place.
Secondly, when you are trying to find the common factor, 1 will always be there doesn’t matter if the number is an even or an odd number.
For even numbers, the first two factors will always be your 1 and 2.
Lastly, for odd numbers, the first two factors will be your 1 and 3.
2. How many factors does number 10 have?
We can divide 10 by following numbers 1,2,5 and 10. All of these numbers can be divided without giving quotient in decimal form. If you look at other numbers such as 3, 4, 6, 7, 8, and 9 you will see they give the quotient in decimal form, meaning 5 is not cleanly divided from these numbers. Thus, 10 has got only 4 factors, and those are 1,2,5 and 10 itself.