In this post, you have at your disposal all the information you need to realize the factorization of 24! Here we will look at how to determine the factors of 24, which should indirectly help you learn methods that will help you determine the factors of any other number that is different from 24. Of course, here we will determine all the factors of 24, while which will include all numbers that satisfy the condition of being factors, regardless of whether they are positive or negative integers. Please note that you are receiving this information as a result of many years of work by a proven mathematics professor.
So let’s factorize 24 using a unique method that you can only see on this page!
Factorization of 24
To carry out a successful and complete factorization of 24, without missing a factor, and to be completely sure of the obtained result, we must approach the work methodically, moving with a certain rule.
We carry out the factorization of 24 following the following method:
We begin with an analysis that begins with the smallest positive number – the number 1 which is a factor of any other integer. In doing so, we form the first pair of factors of the number 24. We know that:
24=1×24
So the numbers 1 and 24 are factors of the number 24!
We continue with number 2! 2 is also a factor of 24 and we all know that we can write the following equation:
24=2×12
So the numbers 2 and 12 are also factors of the number 24!
We continue with number 3! 3 multiplied by 8 is 24, that is:
24=3×8
So the numbers 3 and 8 are factors of the number 24!
We continue with number 4! 4 multiplied by 6 is 24, that is:
24=4×6
We continue with number 5! If we divide 24 by 5 then we will not get a result that is an integer, which means that the number 5 is not a factor of the number 24!
Positive Factors Of 24
If we decide to continue testing the numbers we come to the number 6 which we have already determined is a factor of the number 24. When this happens then it is the right time to stop testing new numbers while making sure we have covered all possible factors of the number 24!
Let’s find out! Positive numbers that are factors of the number 24 are:
1; 2; 3; 4; 6; 8; 12; 24
Negative Factors Of 24
Our obligation remains to determine all the negative numbers that are factors of the number 24. If we recall the rule for multiplying whole numbers, that two numbers with – signs have a product (by multiplying two negative numbers) with a + sign, then no it is difficult to conclude that all numbers opposite in sign to the sequence of positive factors of 24 will also be factors of the number 24!
Let’s find out! Negative numbers that are factors of the number 24 are:
-1; -2; -3; -4; -6; -8; -12; -24
All Factors From Factorization of 24
And finally, finally, all the factors of 24, written in a sequence of numbers, starting with the smallest number and ending with the largest number is:
-24; -12; -8; -6; -4; -3; -2; -1; 1; 2; 3; 4; 6; 12; 24
Factorization Table Of 24
The table below covers the complete factorization of 24, including all possible products of integers that result in 24!
| Factorization Of 24 |
|---|
| 24=1×24 |
| 24=2×12 |
| 24=3×8 |
| 24=4×6 |
| 24=(-1)x(-24) |
| 24=(-2)x(-12) |
| 24=(-3)x(-8) |
| 24=(-4)x(-6) |
In the video below, our readers have a visual representation of our methodology for realizing a comprehensive factorization of 24! If any of you are having trouble understanding the methodology itself from the text on this page, use the video to learn everything you need to do to complete the factorization of 24 completely and without errors!
Use Prime Factorization Decomposition Of 24 To Find Factors Of 24
We can discover the factors of the number 24 in a different way! If we decide to use prime factor decomposition, then let’s look at the branch of prime factors of the number 24 (see how prime factorization is practiced by clicking on the colored text in this sentence)! She looks like this:
It is clearly seen that the number 24 decomposed into its prime multiples can be represented as a product of them in this way:
24=1x2x2x2x3
To find the factors of 24, we need to calculate the products of all possible combinations of its prime factors. That way we get all the positive factors of 24, as we have already indicated above in this text. As soon as we discover all the positive factors in this way, in the sequence of all the factors we also write down their opposites (by sign) negative numbers!
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