Factors Of 24 | Division & Prime Factorization | Easy Guide

The factors of 24 are the integers that divide the original evenly. The remainder will thus be zero. There are more than two 24 factors because it is a composite number. Among all the factors twenty-four, there are 8 following factors:

  1, 2, 3, 4, 6, 8, 12 and 24. For Example

 the factors of 75 are :

1, 3, 5, 15, 25, and 75.

When multiplied in pairs, factor pairs of 24 give a result of 24. If we need to know the pair factor of 24, we will have 4 following pairs:

(1, 24), (2, 12), (3, 8), (4, 6). 

Now, I am going to the prime factor of 24, which gives the following:

2 x 2 x 2 x 3 = 23 x 3, where 2 and 3 are all the prime factorizations of 24. 

Do you know the sum of factors of twenty-four?

Yes!  You are right; Their sum is 60.

In addition to 24 being a multiple of 24, there are multiples of 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, and so on.

One more thing that I have seen is that the factors of an even number will have even factors because Even numbers are multiples of 2, so a factor of 2 will always be 2. Like factors of 24. Similarly, odd numbers will have odd factors like factors of 39 are 1,3,13.

Factors of 24

According to the definition of a factor, a number can be divided into equal parts. Therefore, factors of 24 are such whole numbers that can divide 24 into an equal number of parts.  So, these factors shouldn’t be a fraction.

How many factors does 24 have?

As we know, by prime factorization of factors, we have;

 2 x 2 x 2 x 3 = 23x 3

Therefore, It can be seen that 2 has an exponent of 3, and 3 has an exponent of 1.

Suppose we want to find the number of twenty-four factors; we add 1 to each exponent and multiply them; it is an innovative formula to find out the factor pairs for 24. Here is the process:

(3+1) x (1+1)

= 4 x 2

= 8

Therefore, they have 8 positive factors.

How to Find the Prime Factorization 24?

The division method can be used to find the pair factors of 24. Whenever a number is divided, the factors will always be less or equal to the original number. Therefore, 24 needs to be divided by a smaller number or by itself. The divisor becomes the required factor when the division produces a whole number in maths.

As we know, 1 is the factor of all natural numbers, and you can say a common factor also. Similarly, a number is a factor in itself. Therefore, 1 and 24 are two all the factors of 24 Since 24 is an even number, thus it is divisible by 2. 24/2 = 12, so 2 is a factor. 

24 is also a multiple of 3, 4, 6, 8, and 12. Therefore, the other factor tree of 24 are 3, 4, 6, 8, and 12. Hence,

• 24 ÷ 1 = 24
• 24 ÷ 2 = 12
• 24 ÷ 3 = 8
• 24 ÷ 4 = 6
• 24 ÷ 6 = 4
• 24 ÷ 8 = 3
• 24 ÷ 12 = 2
• 24 ÷ 24 = 1

We get fractions, apart from these eight numbers, if we divide 24 by any other number.

As an example, 24 ÷ 5 = 4.8

Hence, the calculated factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Pair Factors of 24

If we multiply two numbers in pairs to get 24 so by this we can find the factor tree of 24. Such as:

• 1 × 24 = 24 similarly, 24 x 1 = 24
• 2 × 12 = 24 similarly, 12 x 2 = 24
• 3 × 8 = 24 similarly,    8 x 3 = 24
• 4 × 6 = 24 similarly,    6 x 4 = 24

Therefore, the pair factors are (1, 24), (2, 12), (3, 8), and (4, 6).
We can consider negative factor pairs of 24 or, in other words, factors of Negative 24. It is because the product of two negative factors will give positive factors, such as:

• -1 × -24 = 24 similarly, -24 x -1 = 24
• -2 × -12 = 24 similarly, -12 x -2 = 24
• -3 × -8 = 24 similarly,    -8 x -3 = 24
• -4 × -6 = 24 similarly,    -6 x -4 = 24

Therefore, The negative factor pairs of 24 are as follows:

(-1, -24), (-2, -12), (-3, -8), and (-4, -6)

Prime Factor of 24

As we know, 24 is a composite number because it has more than two factors. The next step is to find the prime factors of 24 called prime factorization. Divide the number 24 with 2 because it is the smallest prime factor.

24 ÷ 2 = 12

Again, divide 12 by 2.

12 ÷ 2 = 6

6 ÷ 2 = 3

Factor Tree of 24 by Prime Factorization

• Now, if we divide 3 by 2, we get a fraction number, which cannot be considered a factor.
• Now, proceed to the following prime number, i.e., 3.

3 ÷ 3 = 1

• We have received 1 at the end, and we cannot proceed with the division method. 

So, the prime 24 factor tree is:

2 × 2 × 2 × 3 = 24

23 × 3 = 24

Where 2 and 3 are the prime numbers.

What did You need to Know?

Learn more about factors and prime factors here with us at ECTI.

Factor Pairs Solved Examples

Q.1: What are the common factors of 24 and 25?

The common 24 and 25 factors are as follows:

Factors of 24 = 1, 2, 3, 4, 6, 8, 12 ,24.

Factors of 25 = 1, 5, and 25.

Common Factors: 1

Therefore, 1 is the common factor of 24 and 25.

Q.2: David has 24 chocolates in his bag. He has to distribute the chocolates among his 6 friends. How can he do it? 

Solution:

Number of Candies David has = 24

Number of Friends = 6

Thus, each of the friends will get = 24/6 = 4 chocolates

Q.3: What is the prime factor of 24?

Solution: 

The prime factorization of 24 is as follows:

2 × 2 × 2 × 3 = 24 

23 × 3= 24

Therefore, 2 and 3 are the prime numbers of 24.

Factors and Multiples of 24

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