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.
Factors of 24 | Factor Pairs of 24 | Prime Factorization of 24 |
1, 2, 3, 4, 6, 8, 12, and 24 | 1 x 24 | 2^{3}x 3 |
2 x 12 | ||
3 x 8 | ||
4 x 6 |
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.
1 × 24 = 24 |
2 × 12 = 24 |
3 × 8 = 24 |
4 × 6 = 24 |
6 × 4 = 24 |
8 × 3 = 24 |
12 × 2 = 24 |
24 × 1 = 24 |
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.
-1 × -24 = 24 |
-2 × -12 = 24 |
-3 × -8 = 24 |
-4 × -6 = 24 |
-6 × -4 = 24 |
-8 × -3 = 24 |
-12 × -2 = 24 |
-24 × -1 = 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.
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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.
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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.
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