Factorization is the study of finding the whole numbers which give you the product as a given number when you multiply each other. Maths could be tough for some students, as some are good with numbers, and some are not. But one thing is sure, and when it comes to finding out the factors, it’s an easy score for every student. The questions of finding out the factors are quite easy then other questions which might come in your exam. But you need to make sure that you don’t make any silly mistakes and lose marks in it.
Today we are going to show you the factors of 80 and find out the prime factorization of 80. We will be discussing the importance of factors and will be dropping some cool facts here and there, which makes learning a bit more fun.
Let’s start with the very basic, and here we are going to show the factors of 80. Before we move any further, let’s talk about 80 in the first place. Have you seen a puzzle that has moving parts? Each puzzle that has 15 moving parts can be solved in just 80 single tile moves. In addition to this, 80 is an even, composite, and abundant number. On the other hand, 80 is not your perfect square; neither is your perfect cube.
Now let’s find out the factors of 80; as you can see, 80 is a big number so that you will find plenty of factors for this particular number. A factor is a number which, when multiplied by another whole number, gives you the product that is your given number, and in this case, we have a product i.e., 80.
So, starting our factorization.
These are the only numbers that can make a product of 80, but numbers bigger than 80 will always have a product greater than 80, so there’s no use of going any further. As a result, we have our list of factors of 80, and it looks like this.
These are all factors of 80 =1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
One more interesting fact about 80, in some, find the factor puzzles, 80 is a clue, which can be used to find other numbers in the puzzle, you need to use the 8X10 fact only.
Now let’s look at the question, what is the prime factorization of 80, and how can we find it. See prime factors are those numbers, which are prime in nature, meaning they are only divisible by 1 and the number themselves.
We have found out the factors of 80 now. We need to take out the prime factors and multiply them to get the answer.
From the above solution, we have 1,2,4,5,8,10,16,20,40,and 80 as factors.
Now, we take out prime numbers. First, these two numbers are 2 and 5.
After that, we multiply 2x5, but it only comes out to be 10.
So what we do is, we multiply 2x5 from 3 times 2.
Thus, (2X2X2) X (2X5) = 8 X 10 = 80.
You can also write this as (2)4 *5, and this is your only prime factorization of 80.
So now we have found out the factors of 80 and have understood the concept of prime factorization of 80. We think it’s time we try our hands-on solving some problems related to factors of 80.
Question: Find the common factors of 80 and 100.
Solution: from the question we can see, we have to find the numbers that are present in the factorization of both 80 and 100.
So first let’s see the factors of 80 = 1,2,4,5,8,10,16,20,40,and 80.
In the same way, let’s look at the factors of 100 = 1,2,4,5,10,20,25,50, and 100.
After comparing both, we take out the numbers that are appearing in both factorizations.
Common factors = 1,2,4,5,10 and 20.
We have given you a solved example, and we hope a lot of things have been cleared regarding the factors of 80. Now it’s the right time for you to take out your pen and notebook and try to solve some questions yourself. If you are stuck somewhere, comment down the problem, and we will be happy to help you solve that problem.
1. What is the Product of Factors?
A product is a factor is a number that comes out after two factors multiply to give you a whole number. It may sound a bit tricky, but it’s all the same as finding a factor of a number. This is a once nice technique that is used by teachers in exams to make students think twice before writing an answer.
Example:- In how many ways can you show 6 as the product of its factors?
Solution:- factors of 6 = 1,2,3, and 6.
6 is a composite number thus, 6 = 1X6 and 6 = 2X3.
These are the only two ways from which you can represent 6 as the product of its factors.
2. What Does it Mean By the Greatest Common Factor (GCF)?
A whole number that is the largest positive integer, which leaves remainder 0 when divided with all the numbers present in the sets of factors, is called your greatest common factor. Now the definition may sound a bit confusing, but we are sure with example things will look quite simple.
Example:- 10,20 and 30 are the given numbers, find the greatest common factor of these numbers.
Solutions:- factors of 10 = 1,2,5,and 10
Factors of 20 = 1,2,4,5,10 and 20.
Factors of 30 = 1,2,5,10,15, and 30.
Thus, GCF of 10,20, and 30 is 10, because when you divide 10 from 10, 20, and 30, the remainder will be zero.