Prime Factorization of 24 ⇒ 2 × 2 × 2 × 3 or 2^3 × 3 Distinct Prime Factors of 24 ⇒ 2 and 3 Number of Distinct Prime Factors of 24 ⇒ Two All Prime Factors of 24 ⇒ 2, 2, 2, 3 Number of all the Prime Factors of 24 ⇒ Four Product of all the Prime Factors of 24 ⇒ 2 × 2 × 2 × 3 = 24 Factors of 24 ⇒ 1, 2, 3, 4, 6, 8, 12, 24 Number of all the Factors of 24 ⇒ Eight Positive Factor Pairs of 24 ⇒ (1, 24), (2, 12), (3, 8), (4, 6) Negative Factor Pairs of 24 ⇒ (-1, -24), (-2, -12), (-3, -8), (-4, -6) Sum of all the Factors of 24 ⇒ 60 |
Prime Factorization of 24
Prime Factorization of 24: Division Method
Step 1: Begin dividing 24 by the smallest prime number that can divide 24 evenly. 24 is divisible by 2.
24 ÷ 2 = 12.
Step 2: Next, divide the quotient, 12, by 2 once more.
12 ÷ 2 = 6.
Step 3: Divide the quotient, 6, by 2 again.
6 ÷ 2 = 3.
Step 4: Divide the quotient, 3, by 3.
3 ÷ 3 = 1.
After obtaining a quotient of 1, further steps are unnecessary.
Therefore, the Prime Factorization of 24 by division method is 2 × 2 × 2 × 3.
This can also be written in exponential form as 2^3 × 3 where 2 and 3 are the prime factor of 24.
Prime Factorization of 24: Factor Tree Method
To find the prime factorization of 24, you can use the factor tree method. In this method, we create branches with prime numbers that divide the number 24. The numbers at the end of the branches are the prime factors of 24, and by multiplying all these prime factors we get a prime factorization of 24.
- Step 1: Consider the 24 as the root of the tree.
- Step 2: Write 2 and 12 pair of factors as the branches of a root of a tree which is 24.
- Step 3: As 2 is a prime number, we circle it as a prime factor in the prime factorization of 24 as illustrated in the image above.
- Step 4: Move on to 12, which is a composite number, so again factorize 12, and write down 2 and 6 pair of factors as the branches of a tree, as 2 is a prime number, we highlight it as one of the prime factors of 24 as shown in the image above.
- Step 5: Move on to 6, which is a composite number, so again factorize 6, and write down 2 and 3 pair of factors as the branches of a tree, Since 2 and 3 are the prime numbers we circle it as one of the prime factors of 24. Now stop here as 2 and 3 are the prime numbers that cannot be divided by any number other than 1 and themselves. The factor tree ends here.
Therefore, the Prime Factorization of 24 using factor tree = 2 × 2 × 2 × 3, which can also be written in exponential notation as 2^3 × 3, where 2 and 3 are prime factors of 24.
Prime Factors of 24
To find the number of prime factors of 24, we need to consider each unique prime factor in its prime factorization of 24.
The prime factorization of 24 is 2^3 × 3 (or 2 × 2 × 2 × 3)
There are two distinct prime factors in the prime factorization of 24: 2 and 3.
Prime Factors of 24: Product
The prime factorization of 24 is represented as 2 × 2 × 2 × 3 (or 2^3 × 3).
To find the product of all the prime factors of 24, we simply multiply these prime factors together:
24 as a product of prime factors = 2 × 2 × 2 × 3 = 24. Therefore, the product of all the prime factors of 24 is 24.
Finding All Factors of 24 using Prime Factorization
The factors of 24 are those numbers that divide the number 24 completely without leaving any remainder.
The prime factorization of 24 represents the product of its prime factors, and every factor of 24 can be obtained by taking combinations of these prime factors.
To find all the factors of 24 using the prime factorization method, follow these steps:
- Write the prime factorization of 24.
- Write down all possible combinations of the prime factors of 24.
- Find all the factors of 24 by calculating the product of each combination.
Step 1: Write the prime factorization of 24 as a product of its prime factors:
24 = 2 × 2 × 2 × 3 or 2^3 × 3
Step 2: Combinations of the prime factors of 24:
- Combination 1: 1
- Combination 2: 2
- Combination 3: 3
- Combination 4: 2 × 2
- Combination 5: 2 × 3
- Combination 6: 2 × 2 × 3
- Combination 7: 2 × 2 × 2
- Combination 8: 2 × 2 × 2 × 3
Step 3: Find all the factors of 24 by calculating the product of each combination.
- Factor 1: 1 = 1
- Factor 2: 2 = 2
- Factor 3: 3 = 3
- Factor 4: 2 × 2 = 4
- Factor 5: 2 × 3 = 6
- Factor 6: 2 × 2 × 3 = 12
- Factor 7: 2 × 2 × 2 = 8
- Factor 8: 2 × 2 × 2 × 3 = 24
Therefore, the factors of 24 are as follows: 1, 2, 3, 4, 6, 8, 12, and 24
Pair Factors of 24
To find the pair factors of 24, you can list all the possible pairs of numbers that multiply together to give the product of 24:
| Positive factor pairs of 24 | Negative factor pairs of 24 |
|---|---|
| 1 × 24 | (-1) × (-24) |
| 2 x 12 | (-2) x (-12) |
| 3 x 8 | (-3) x (-8) |
| 4 x 6 | (-4) x (-6) |
The product of each pair is equal to 24, which makes these pairs the factor pairs of the number 24.
Counting Factors of 24 using Prime Factorization
To find how many factors there are in 24, you can find the prime factorization of 24 and then use the formula to calculate the total number of factors in 24.
The prime factorization of 24 is 2 × 2 × 2 × 3 (or 2^3 × 3)
To calculate the number of factors in 24, use the formula:
Number of factors = (Exponent of 1st prime factor + 1) x (Exponent of 2nd prime factor + 1) x … x (Exponent of nth prime factor + 1)
In this case:
Number of factors = (3 + 1) x (1 + 1) = 4 x 2 = 8
So, there are 8 factors in 24 which are 1, 2, 3, 4, 6, 8, 12, and 24. These numbers divide evenly the number 24 without leaving any remainder.
The Sum of All Factors of 24
To find the sum of all factors of 24 using its prime factorization, we first list all the factors as obtained from the prime factorization of 24:
We have already obtained all the factors of 24 using its prime factorization.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24
Now, sum all these factors: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60
Therefore, the sum of all factors of 24 is 60.
Related Examples
Example 1: What is the prime factorization of 36?
The prime factorization of 36 is 2^2 x 3^2, where 2 and 3 are the prime factors.
Example 2: What are the factors of 24?
The factors of 24 are listed as: 1, 2, 3, 4, 6, 8, 12, and 24.
Example 3: What are the factors of 18?
The factors of 18 include: 1, 2, 3, 6, 9, and 18.
Example 4: What are the factors of 12?
The factors of 12 are: 1, 2, 3, 4, 6, and 12.
Example 5: What are the factors of 40?
The factors of 40 are listed as: 1, 2, 4, 5, 8, 10, 20, and 40.
Example 6: What are the factors of 20?
The following numbers are the factors of 20: 1, 2, 4, 5, 10, and 20
Example 7: What are the factors of 16?
The factors of 16 are: 1, 2, 4, 8, and 16.
Example 8: What are the factors of 27?
The factors of 27 are as follows: 1, 3, 9, and 27.
FAQs on Prime Factorization of 24
Q1 How do you write the prime factorization of 24 using powers?
The prime factorization of 24 using powers can be written as 2^3 x 3, where 2 and 3 are the prime factors.
Q2 What is the prime factorization of 24 and 8?
Prime factorization of 24 using exponents is 2^3 x 3 or (2 x 2 x 2 x 3)
Prime factorization of 8: 2^3
Q3 What is the prime factorization of 24 step by step?
Step 1: Begin with the smallest prime factor, which is 2. Perform a division of 24 by 2, resulting in 12.
Step 2: Now, divide 12 by 2 to get 6.
Step 3: Divide 6 by 2 to get 3. Since 3 is a prime number, the factorization stops here.
Prime factorization of 24: 2^3 x 3
Q4 What is the prime factorization of 24 using the factor tree?
The prime factorization of 24 using a factor tree method is as follows:
24
/\
2 12
/\
2 6
/\
2 3
Prime factorization of 24: 2^3 x 3
Q5 What is the prime factorization of 12 and 24?
Prime factorization of 12: 2^2 x 3
Prime factorisation of 24: 2^3 x 3
Q6 What is the prime factorization of 22 and 24?
Prime factorization of 22: 2 x 11
Prime factorization of 24: 2^3 x 3
Q7 What are the prime factors of 24
The prime factors of 24 are represented by 2 and 3. The prime factorization of 24 can be written as 2^3 x 3, where 2 is raised to the power of 3 and 3 is raised to the power of 1.
Q8 What are the Prime Factors of 24?
The prime factors of 24 are represented by 2 and 3. The prime factorization of 24 is expressed as 2^3 * 3, where 2 is raised to the power of 3 and 3 is raised to the power of one.
Q9 Find the sum of the factors of 24.
To find the sum of the factors of 24, we can list all the factors and add them up:
The factors of 24 comprises the numbers 1, 2, 3, 4, 6, 8, 12, and 24.
Sum of the factors: = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60
So, the sum of the factors of 24 is 60.
Q10 How many exponents of 3 will be there in the prime factorization of 24?
To find the number of exponents of 3 in the prime factorization of 24, we need to determine how many times the prime factor 3 appears in the factorization.
The prime factorization of 24 is 2^3 x 3^1.
As we can see, the exponent of 3 is 1.
Therefore, in the prime factorization of 24, there is 1 exponent of 3 (i.e., 3^1).
Q11 What is the prime factorization of 30, 32, and 60?
The prime factorizations of 30, 32, and 60 are as follows:
- Prime factorization of 30 is 2 x 3 x 5
- Prime factorization of 32 is 2^5 (or 2 x 2 x 2 x 2 x 2)
- Prime factorization of 60 is 2^2 x 3 x 5 (2 x 2 x 3 x 5)