Know the Factors of 24 on Vedantu
Factors of 24 are all the Integers, both positive and negative whole Numbers which you can evenly divide by the Number 24. 24, when divided by a Factor of 24 would lead you to another Factor of 24. You can also say that the Factors of 24 are the Numbers that give you the result as the Number 24 when you multiply Numbers together in a pair. You can also say that if a Number divides the Number 24 and gives you a zero remainder, it is called a Factor of 24. Given below are the Factors of 24 and their pair Factors.
Factor Pairs of 24
The Factor pairs of 24 are all the possible combinations of two Factors which when multiplied together equal to 24. There are both positive and negative Factor pairs of 24. Given below are all the positive Factor pairs of 24 that you should know about.
Likewise, the Factors of 24 include negative Numbers as well. Minus times minus equals to plus, therefore, you can convert the positive Factor pair by simply inserting a minus sign in front of every Factor and get all the possible negative Factor pairs of 24.
Prime Factorization of 24
Since 24 is a composite Number, you can find its Prime Factors by following the simple division as follows.
First, divide 24 with the smallest Prime Factor which is the Number 2.Doing so, you get, 24 ÷ 2 = 12
Again, divide the Number 12 by 2 since it is a composite Number.Doing so you get, 12 ÷ 2 = 6
Dividing further, you get 6 ÷ 2 = 3
Now, if you try to divide 3 by 2, you would get a fraction Number that cannot be a Factor.
Hence, you need to proceed to the next Prime Number which is 3. Dividing the Number 3 by itself, you get, 3 ÷ 3 = 1
Now, you have received 1 at the end and you cannot proceed further with the division method.
Therefore, the Prime Factorization of 24 is written as 2 × 2 × 2 × 3.
You can also write it as 23 × 3, wherein, 2 and 3 are the Prime Numbers.
Prime Factorization is a way by which Factors of any Number can be found out. Prime Factorization is taught in schools from the fifth standard. It forms the foundation of mathematics. In order to ace the exam, students are advised to study this concept in-depth as this will help them in higher studies.
The expert mathematics teachers at Vedantu have curated all the important Factors of various Numbers. This article mainly deals with Factors of 24.
Factors of 24 can be defined as the Integers that divide the Number uniformly. So that there is no remainder left. The total Number of Factors of 24 are eight, they are 12346 8,12 and 24. As 24 is a composite Number it has Factors more than two.
There are pair Factors of 24 these are the Numbers which when multiplied together give the result 24. Its pair Factors are – (1,24) (2,12) (3,8) (4,6).
Factor Pairs of 24-
Factor pairs are Numbers which when multiplied together give 24 as a result. The Factors are both positive and negative. Given below are the positive Factor pairs of 24 –
1 x 24 = 24
2 x 12 = 24
3 x 8 = 24
4 x 6 = 24
6 x 4 = 24
8 x 3 = 24
12 x 2 = 24
24 x 1 = 24
Factors of 24 = 1,2,3,4,6,8,12, and 24
The Factors of 24 include negative Numbers as well. By simply inserting a minus sign in front of every positive Factor, students can get all the possible negative Factor pairs of 24. They are as follows –
-1 x -24 = 24
-2 x -12 = 24
-3 x -8 =24
-4 x -6 = 24
-6 x -4 = 24
-8 x -3 = 24
-12 x -2 = 24
-24 x -1 = 24
Prime Factorization of 24
The Prime Factors of 24 can be found easily as 24 is a composite Number.
Step 1 is to divide 24 with the smallest Prime Factor which is 2=
24 ÷ 2 = 12
Step 2 is to divide the Number 12 by 2 since it is a composite Number =
12 ÷ 2 = 6
Step 3 is to divide the Number further by 2 =
6 ÷ 2 = 3
Now, 3 cannot be divided b2 as it will lead us to a fraction Number which cannot be a Factor,
Therefore, to proceed, step 4 will be to divide 3 by itself =
3 ÷ 3 = 1
1 cannot be divided further, therefore the Prime Factors of 24 are = 2 x 2 x 2 x 3 = 23 x 3, where 2 and 3 are Prime Factors.
FAQs on Factors of 24
1. List all the Factors of 24
The factors of 24 include both the positive and the negative integers. Hence, the positive factors of 24 are:
1, 2, 3, 4, 6, 8, 12, 24.
The negative factors of 24 include the following Numbers:
-1, -2, -3, -4, -6, -8, -12, -24.
2. What is the Prime Factorization of 24?
Factoring a Prime Number means finding all the Prime Numbers that are the factors of that particular Number. You can write a composite Number as a product of all its Prime factors.
You can write the Number 24 as the product of the Prime Numbers.
When you multiply 2 x 2 x 2 x 3, it gives you 24 as a result.
A factor tree is a method that shows the Prime factors of a composite Number in the form of a tree. Drawing factor trees is a great method for performing the Prime factorization of any given Number.
You can make different factor trees for finding the same Prime factorization of the given Number. Take a look at these two examples below for finding the Prime factors of 24.
Both these factor trees give you the same Prime factorization of 24.
You can write the Prime factorization of 24 as 2 x 2 x 2 x 3 or 2³ x 3.
3. What are the Prime Factors of 24?
The Prime factors of 24 are all the Prime Numbers which divide by the Number 24 exactly without having any remainder. In simpler words, a Prime factor of 24 divides the Number 24 and gives the remainder as 0.
For the Number 24, the Prime factors are 2, and 3. By the definition of a Prime Number, 1 is not regarded as a Prime Number.
Besides the Number 1, the thing that differentiates all the factors from the Prime factors of the Number 24 apart is the word Prime. The former list of factors contains both, the composite and the Prime Numbers, whereas the latter Prime factors consist of only the Prime Numbers.
4. How can I find Factors of 24?
24 being an even Number, when divided by other even Numbers can get us Factors of 24-
24 ÷ 1 = 24
24 ÷ 2 = 12
24 ÷ 3 = 8
24 ÷ 4 = 6
24 ÷ 6 = 4
24 ÷ 8 = 3
24 ÷ 12 = 2
24 ÷ 24 = 1
Therefore, we get the Factor of 24 by dividing it with even Numbers which do not leave a remainder. The Factors of 24 are - 1, 2, 3, 4, 6, 8, 12, and 24.
5. Where can I find study material related to Factors of 24?
The study material related to Factors of 24 is available on Vedantu's website which is specially curated for students wanting to get a higher score in the examinations. This study material acts as a reference guide and can be read online or offline as it is available in a PDF format for free download.
6. What is Prime Factorization?
Expressing a Number as a product of its Prime Factors is called Prime Factorization. A Prime Number has only two Factors that are one and the Number itself, for example we can say that 2 is a Prime Number having only two Factors that is two and one, on the other hand, a composite Number has more than two Factors.
7. What are the Numbers of Factors of 24?
Factors of 24 can be found out by using Prime Factorization-
Factors of 24 are – 2 x 2 x 2 x 3 = 23 x 3 the exponent of 2 is 3 and 3 is 1 by adding 1 and then multiplying the exponents we will be able to get the Factors of 24 –
(3+1) x (1+1)
= 4 x 2
= 8
Therefore, we get that there are 8 Factors of 24.
8. What are the pair Factors of 24?
The pair Factors of 24 are both positive and negative. They are as follows-
1 x 24 = 24
2 x 12 = 24
3 x 8 = 24
4 x 6 = 24
6 x 4 = 24
8 x 3 = 24
12 x 2 = 24
24 x 1 = 24
Factors of 24 = 1,2,3,4,6,8,12, and 24
Negative Factors-
-1 x -24 = 24
-2 x -12 = 24
-3 x -8 =24
-4 x -6 = 24
-6 x -4 = 24
-8 x -3 = 24
-12 x -2 = 24
-24 x -1 = 24
Therefore, the negative Factors are -1, -2, -3, -4, -6, -8, -12, -24.