Factors of 24 – With Division and Prime Factorization

Factors of 24

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

  1, 2, 3, 4, 6, 8, 12 and 24. 

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, come 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 factors 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.

What are the 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.

What are the Factors of 24?

What are the Factors of -24?

There are some negative pair factors that we can get by -24 by having (-1, 24), (-2, 12), (-3, 8), and (-4, 6) as a pair of factors. Similarly, we can also get -24 by having (1, -24), (2, -12), (3, -8), and (4, -6) as a pair of factors. These all are negative numbers.

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 factors of 24. Here is the process:

(3+1) x (1+1)

= 4 x 2

= 8

Therefore, they have 8 positive factors.

How to Find Factors of 24?

The division method can be used to find the 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.

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 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 factors 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.

Factors of 24 By Division Method

Pair Factors of 24

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

pair Factors of 24
  • 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 -24. It is because the product of two negative factors will give a 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

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 factors of 24 are:

2 × 2 × 2 × 3 = 24

23 × 3 = 24

Where 2 and 3 are the prime numbers.

What did You need to Know?

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Prime factors of 24: 2 and 3 Pair factors of 24: (1, 24), (2, 12), (3, 8), and (4, 6).Prime factorization of 24: 23 × 3

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

Factor Pairs Solved Examples

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

The common factors of 24 and 25 are as follows:

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

Factors of 25 = 1, 5, 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 are as follows:

2 × 2 × 2 × 3 = 24 

23 × 3= 24

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

Factors and Multiples of 24

Factors of 24Multiples of 24
1, 2, 3, 4, 6, 8, 12 and 2424, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, etc.

FAQ’s

What are the factors of 24?

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

How many factors does 24 have?

There are 8 factors in total about 24: (1,2,3,4,6,8, 12, 24)

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

How to find the number of factors?

With prime factorization, we can find the factors of a number.

  • The next is to check the number of exponents.
  • Add 1 to each exponent and multiply them all together.

For example, the prime factorization of 8 is 2 x 2 x 2 = 23. The exponent, in this case, is 3. Therefore, we have 4 factors since 3+1 = 4.

What are the prime factors of 24?

The prime factorization of 24 is 2 × 2 × 2 × 3 = 23 × 3 and there are some factors of 24 in pairs that are : (1,24), (2,12) (3,8) and (4,6).

What are two factors equal to 24?

We have the following two factors in pairs, which gives 24.

  • 1 x 24 = 24
  • 2 x 12 = 24

What times give 24 as result?

Solution:

1 x 24 = 24 ( one times twenty-four is equal to twenty-four)

2 x 12 = 24 ( Two times twelve is equal to twenty-four)

3 x 8 = 24 ( Three times eight is equal to twenty-four)

4 x 6 = 24 ( four times six is equal to twenty-four)

What are the positive factor pairs of 25?

Factor 25: 1-5

What are the Positive factors of 24?

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

What are factor pairs of 24?

The two factors are (2, 122). 24 + 2 = 7. Three and eight factor also exist. 23 x 4 = 5. There are also six factors for each. 25 = 5 = 47. … -2 -3-4 -3 -4 -6 -9 -12 -24. 23 – 2 + 2. 122 = 6.

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