Factors of 24 – Methods To Find All Factors of 24

Factors of 24 are those positive and negative whole numbers that can easily divide into 24. When you divide any factor of 24 by 24 till you reach 0 as a dividend it leads to another factor of 24.

24 factors are those pairs of numbers that product or multiplication give you a result of 24.

There are a total of 8 factors of 24 of which number 24 is the biggest factor and 2 is the smallest. 

Here you will find all the information related to the prime factorization of 24. We will provide you with how to find the factors for 24, and how many 24 factors are there. You will get the answer of factor pairs of 24, prime factorization of 24, and factor tree of 24 in the article.

All factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24 in which 24 is the biggest factor and 2 & 3 are prime factors for 24.

Definition – Factors Of 24

The factors of 24 are the combination of integers (Integers are all positive and negative whole Numbers) that can divide 24 evenly.

According to the definition of the 24 factors, there are 8 main factors of 24 that are evenly divided by 24 without remainder.

What Are The Factors Of 24?

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24 in which 24 is the biggest factor and 2 & 3 are prime factors for 24. (Prime factor is a factor that is divided by 1 or a number itself without any remaining remainder). 

You can say if two numbers are multiplied and the result of the pair is 24 then the numbers are the pair factors of 24.

As We mentioned above in this factor list you can consider both negative and positive numbers. So, the prime 24 factors are negative numbers also such as -1, -2, –3, -4, -6, -8, -12, and -24.

For example, if you multiply a negative pair of factors by 24 and the result is 24 then it’s a factor of 24. Such as (-12) x (-2) = 24 so -12 and -2 are Pair of 24 Factors.

How To Find All Factors of 24?

To find the prime factors of 24 you can apply multiple methods. All the methods are simple to apply through which you can find all the Factors of 24 easily. 

• Factors of 24 using Multiplication Method
• Prime Factorization of 24
• Factor Tree of 24

Factors of 24 Using Multiplication Method

By using the following steps mentioned below you can find the factors for 24 using multiplication methods.

Step 1 – To find the 24 factors using the multiplication method you need to check what pairs of number products are 24. Just divide 24 from 1 to 24 natural numbers. Divide the number and make a note of all the numbers that completely divide 24 without the remaining remainder.

Step 2 – The number list out outcomes that completely divide 24 are the factors of 24. After finding the number we have to write them in a pair that products show 24 as a result. We have listed the pair below for clarification. We find the 8 factors of 24 when we divide the number from the natural number 1 to 9.

For Example, the list of factors starts from 1 so the calculation will be – 1 X 24 = 24, 2 X 12 = 24, 3 X 8 = 24, 4 X 6 = 24. 

If we write these 24 factors in a pair form then the list goes as (1, 24), (2, 12), (3, 8), and (4, 6). The mentioned are the pair factors of 24.

So, the result shows that if we write 1 as a factor of 24 then we get another factor is 24, if you write 2 as a factor of 24 then you will get 12 as the other 24 factors. The list of the factors goes on till we find the 8 main factors of 24.

Step 3 – After completing this method we find a list of factors of 24 starting from 1 and ending at 24. Through this method, we can easily find the factors of the 24 listed below. 

There are the factors of 24 we have found after the above-mentioned multiplication methods are 1, 2, 3, 4, 6, 8, 12, and 24.

Now let’s move ahead to the other methods of prime factorization of 24 to find 24 factors.

Prime Factorization Method To Find Factors Of 24

Before knowing about the factors of 24 by using prime factorization methods let’s know about what is Prime factorization.

Prime Factorization Is a method of finding the prime numbers, which are multiplied together to get the original number product.

You can easily find the Prime factorization of 24 by using the simple Prime Factorization mentioned steps.

Steps 1 – As You read above that a prime factor is a prime number that is only divisible by itself or 1. To find the prime factors of 24 you have to divide 24 by the smallest prime number. 

With the help of the divisibility rule, you can find the least factor of 24. The first prime factor of 24 is 2. It shows that 2 is the smallest prime factor of 2 by 24 ÷ 2 = 12.

Step 2 – To find the prime factorization you need to repeatedly divide the quotient by 2. Repeat the process until you get the number not divisible by 2. 

Step 3 – Divide the 12 ÷ 2 = 6, You got 6 later Divide 6 by 2, 6 ÷ 2 = 3. Now you will get a quotient that is no more divided by 2 which is 3.

Step 4 – Divide the remaining quotient by 3 which is 3 ÷ 3 = 1. When you get 1 as a quotient then the process is ended and you do need to follow the dividing process.

Steps 5 – You can express the Prime factorization of 24 in two ways 2 x 2 x 2 x 3 or 2³ x 3. Via this, you can find that 2 and 3 are the prime number & prime factors of 24. 

Factors Tree of 24

The other easiest way to find the factors of 24 is the use of a factor tree. The tree factors of 24 draw by factorizing 24 until you get prime factors.

We called this factors tree because in this you split the factor and write in the form of branches of the tree.

In the branches, you will get the final result and the prime factors of 24. To make it easy for you let’s explore the below-mentioned steps and see the below-mentioned chart for clarification.

Step 1 – Split 24 into two factors 2 and 12 Then check which is the prime in between these two. As you read that prime number are those number which is divisible by 1 or itself. So here 2 is the prime factor so circle it and move ahead to split 12.

Step 2 – Split the branches into two below the 12 and find the factors of 12 that are 2 and 6. So in this branch 2 is the prime factor so circle it and split 6.

Step 3 – When you split 6 into branches then the result is 2 and 3. Here we end with the two prime number that is 2 and 3. So circle both numbers because you know that they are not possible to factorize. 

This result is the end of the factor Tree of 24.

Step 4 – So at the end, the prime factors of 24 are 2 x 2 x 2 x 3 = 24. 

You can also split the number into different forms but the result will be the same. You can split 24 into 4 and 6. Later split 4 into 2 and 2 or 6 into 2 and 3. Still, the factor you find is the same is 2 x 2 x 2 x 3 and, the outcome is 24.

Let’s move ahead and find the Factor pair of 24.

Positive And Negative Factors of 24 In Pairs

As you read above that when you have to find the factors of 24 you can consider all the integers that are positive and negative numbers. You can also write these factors in pairs and the product of these factors of 24 is always 24. The below-mentioned table will show you all the Positive Factor Pairs of 24. 

Positive Factors of 24 in Pairs

Above we have introduced you to the positive prime factors of 24. The factor of 24 may have a negative number also. Because the product of two negative numbers always has a positive result.

Negative Factors Pairs of 24

What You Will Observe Via These Factor Pairs Of 24?

In the above-mentioned table of the factor Pairs of 24 you will get the following result:-

• The positive and negative factors of 24 are (1, 24), (2, 12), (3, 8), and (4, 6) or (-1, -24), (-2, -12), (-3, -8), and (-4, -6).
• The factors of any number can be positive or negative.
• Factors of Any number cannot be fractions and decimal numbers.
• The factors of the 24 are the whole numbers the product result is always 24.

Trick To Calculate Total Number Of Factors of 24 or Any Other Number

If you want to know how many total factors of a number are there to check whether your answer is right or not you can follow the steps. The trick will help you to find the number of factors.

As you find factors of 24 by the prime factorization method and the answer is 24 = 2 x 2 x 2 x 3 = 2³ x 3. The prime factorization of the 24 is 2³ x 3.

To find the total factors add 1 in the exponents 3 and 1 individually. Latest multiple the sum for example (3 + 1) x (1 + 1) = 4 x 2 = 8. The answer shows that 24 have 8 factors.

What Are The Factor Pairs of 24?

The factor pairs of 24 are (1 x 24), (2 X 12), (3 X 8), and (4 X 6). You can also write them with negative sign to get factor pairs of negative 24 or (-24).

What Are The Factors And Multiples of 24?

The first five multiples of 24 are 24, 48, 72, 96, and 120. Though the all factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Conclusion

• The factors given are always equal to the number or less than the number.
• Composite Numbers have more than two factors (Composite numbers are number that has more than two factors or you can say the opposite of prime numbers are composite numbers). Therefore 24 is a composite number because it has more than 2 factors.
• The number of factors is finite and you saw that 24 has 8 factors. Such as 1, 2, 3, 4, 6, 8, 12, and 24.
• Those numbers that are completely divided by 24 without leaving any remainder are the Factors of 24.

Let’s List All The Factors of 24

In the end, let’s list the factors of 24 and the prime factorization of the 24 you have solved by using the above-mentioned methods.

• Total Factors: 8
• Positive Factors: 1, 2, 3, 4, 6, 8, 12, and 24.
• Negative Factors: -1, -2, -3, -4, -6. -8, -12, and -24.
• Prime Factors: 2 and 3
• Prime Factorization of 24: 2³ x 3 = 2 x 2 x 2 x 3
• Sum Of Factors: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60

How Will You List The All 24 Factors?

All factors of 24 can be listed as 1, 2, 3, 4, 6, 8, 12, and 24. The sum of all these factors is 60.

What Are The Positive & Negative Factors of 24?

The positive 24 factors are 1, 2, 3, 4, 6, 8, 12, and 24 and the negative factors of 24 are -1, -2, -3, -4, -6. -8, -12, and -24.