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Factors of 48
Factors of 48 are the list of integers that can be evenly divided into 48. It has a total of 10 factors of which 48 is the biggest factor and the prime factors of 48 are 2 and 3. The Prime Factorization of 48 is 2^{4} × 3.
 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
 Negative Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
 Prime Factors of 48: 2, 3
 Prime Factorization of 48: 2 × 2 × 2 × 2 × 3 = 2^{4} × 3
 Sum of Factors of 48: 124
What Are the Factors of 48?
Factors of 48 are the numbers that, when multiplied together, result in 48.
6 × 8 = 48
48/8=6
Here 6 and 8 are multiplied together to get 48.
Hence, we say that 6 and 8 are the factors of 48.
48 has many other factors too as 6 and 8 have factors themselves.
To find them, you can arrange these numbers in arrays as follows.
You may arrange 48 in arrays as above and find the factors of 48.
How to Calculate the Factors of 48?
Step 1: Write down the number to be factored, i.e., 48.
It is a composite number. It can be factored further.
Step 2: Find the two numbers whose product gives 48.
2 × 24 = 48. So, let's take 2 and 24 as the two factors.
2 is a prime number. Hence, it can only be factored as 1 and the number itself.
1 × 2 = 2
Step 3: Since 24 is not prime, let's break it down into factors.
2 × 12 = 24. So, let's take 2 and 12 as the two factors.
Again, 2 is a prime number.
Step 4: Break 12 into factors.
3 × 4 = 12
2 is a prime number.
Step 5: Break 4 into factors.
2 × 2 = 4
We stop here as we have found all the factors of 48.
Hence, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Tips and Tricks:
 1 is the smallest factor of every number.
 Every number has a minimum of 2 factors, i.e., 1 and the number itself.
 All even numbers always have 2 as one of their factors.
Explore factors using illustrations and interactive examples.
 Factors of 36  The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 24  The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
 Factors of 15  The factors of 15 are 1, 3, 5, 15
 Factors of 45  The factors of 45 are 1, 3, 5, 9, 15, 45
 Factors of 72  The factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, 72
 Factors of 49  The factors of 49 are 1, 7, 49
Factors of 48 by Prime Factorization
If the factors of a number are prime numbers, then the factors are said to be prime factors.
Prime factorization is the process of writing a number as a product of its prime factors.
Factors of 48 by prime factorization are given using the following steps.
Step 1: Write the pair of factors that, on multiplication, give the required number.
48 can be factored as a product of 6 and 8.
Step 2: See the factors, whether each one of them is prime or not.
6 is not a prime number and can be factored in as a product of 2 and 3.
8 is not a prime number and can be factored in as a product of 2 and 4.
4 is not a prime number and can be factored in as a product of 2 and 2.
Step 3: As per the criterion,
48 can thereby be written as:
48 = 6 × 8 = 2 × 3 × 2 × 2 × 2
It can also be written as:
48 = 2^{4} × 3^{1}
We can also find the prime factors by this division method or the factor tree method.
Factors of 48 by Division Method
We divide the number every time in such a way that a divisor is a prime number as below.
48 = 2^{4} × 3
Factors of 48 by Factor Tree Method
Can you draw the tree in a quite different way?
Finally, you will get the same prime factorization as 48= 2^{4} × 3^{1}
Challenging Questions:
What are the factors of the following numbers using the prime factorization method?
 96
 245
 6400
Factors of 48 in Pairs
Factor pairs are found in this rainbow method.
Positive Pair Factors of 48
Factors  Pair Factors 

1 × 48 = 48  1, 48 
2 × 24 = 48  2, 24 
3 × 16 = 48  3, 16 
4 × 12 = 48  4, 12 
6 × 8 = 48  6, 8 
Negative Pair Factors of 48
Factors  Pair Factors 

1 × 48 = 48  1, 48 
2 × 24 = 48  2, 24 
3 × 16 = 48  3, 16 
4 × 12 = 48  4, 12 
6 × 8 = 48  6, 8 
Important Notes:
 Factors of any number are all the possible divisible numbers. They may be prime numbers or composite numbers.
 Factors are never fractions or decimals.
 Factors can be negative.
Factors of 48 Solved Examples

Example 1: If Kyle takes 48 hours to finish reading a book in 8 days, find how many hours has she taken per day?
Solution:
We find that 8 × ____ = 48
Now let's find the missing factor.
Using the multiplication fact, we know that 8 × 6 = 48
Hence, Kyle takes 6 hours per day.

Example 2: Can you find the common factors of 45 and 48?
Solution:
The factors of 45 are 1, 5, 9, 45
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The common factor is 1
Hence, the common factor is 1.

Example 3: Help Keath to find the highest common factor of 18 and 12 by prime factorization.
Solution:
Write the prime factorization for each number.
18 = 2 × 3 × 3
12 = 2 × 2 × 3
Next, find the common factors shared by both of the numbers.
The common factors are 2 × 3
The common factor is 6.
Hence, the highest common factor of 18 and 12 is 6.
FAQs on Factors of 48
What are the Factors of 48?
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 and its negative factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
What is the Greatest Common Factor of 48 and 13?
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 and the factors of 13 are 1, 13. 48 and 13 have only one common factor which is 1. This implies that 48 and 13 are coprime.
Hence, the Greatest Common Factor (GCF) of 48 and 13 is 1.
What is the Sum of all the Factors of 48?
Sum of all factors of 48 = (2^{4 + 1}  1)/(2  1) × (3^{1 + 1}  1)/(3  1) = 124
What are the Pair Factors of 48?
The pair factors of 48 are (1, 48), (2, 24), (3, 16), (4, 12), (6, 8).
How Many Factors of 48 are also common to the Factors of 22?
Since, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 and the factors of 22 are 1, 2, 11, 22.
Hence, [1, 2] are the common factors of 48 and 22.
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