Factors of 48 With Examples
Factors of 48 are the numbers that give the original number when multiplied together in pairs or we can say, the numbers which divide 48 completely, leaving zero as a remainder, are its factors. The factors of 48 can be positive or negative. For example, the factors of 48 can be (1, 48) or (1, 48). If we multiply the pair of negative factors, such as multiplying 1 and 48, it will result in the original number 48. Here, we will learn the factors of 48 and the pair factors and the prime factors of 48 using the prime factorization method with many solved examples.
What are the Factors of 48?
The factors of 48 are the numbers that divide 48 exactly without leaving any remainder. In other words, the factors of 48 are the numbers that are multiplied in pairs resulting in an original number. As 48 is an even composite number, 48 has many factors other than 1 and 48. Thus, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. Prime Factorization of 48: 2×2×2×2×3 or 2^{4} × 3. 
Pair Factors of Forty Eight
The pair factors of Forty Eight are the numbers in which the pair of numbers are multiplied together resulting in an original number 48. As discussed above, the pair factors of Forty Eight can also be positive or negative. Thus, the positive and negative pair factors of Forty Eight are given below:
Positive Pair Factors of Forty Eight:
Positive Factors of Forty Eight 
Positive Pair Factors of Forty Eight 
1 × 48 
(1, 48) 
2 × 24 
(2, 24) 
3 × 16 
(3, 16) 
4 × 12 
(4, 12) 
6 × 8 
(6, 8) 
Negative Pair Factors of Forty Eight:
Negative Factors of Forty Eight 
Negative Pair Factors of Forty Eight 
1 × 48 
(1, 48) 
2 × 24 
(2, 24) 
3 × 16 
(3, 16) 
4 × 12 
(4, 12) 
6 × 8 
(6, 8) 
Factors of Forty Eight by Division Method
In the division method, the factors of Forty Eight can be found by dividing 48 by different consecutive integers. If the integer divides 48 exactly and leaves the remainder 0, then the integers are the factors of Forty Eight. Now, let us discuss how to find the factors of the division method.


 48/1 = 48 (Factor 1 and Remainder = 0)
 48/2 = 24 (Factor 2 and Remainder = 0)
 48/3 = 16 (Factor 3 and Remainder =0)
 48/4 = 12 (Factor 4 and Remainder =0)
 48/6 = 8 (Factor 6 and Remainder =0)
 48/8 =6 (Factor =8 and Remainder =0)
 48/12 = 4 (Factor =12 and Remainder =0)
 48/16 = 3 (Factor = 16 and Remainder =0)
 48/24 = 2 (Factor = 24 and Remainder =0)
 48/48 = 1 (Factor = 48 and Remainder =0)

Thus, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
If we divide 48 by any numbers other than 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48, it leaves a remainder, and hence, they are not the factors of Forty Eight.
Prime Factorization of 48
The number 48 is a composite number. Now let us find the prime factorisation of it.


 The first step is to divide the number 48 with the smallest prime factor,i.e. 2.

48 ÷ 2 = 24


 Now, check whether 24 can be further divided by 2 or not.

24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3


 As 3 cannot be divided by 2 because factors are the whole numbers and not the fraction.
 Therefore, we need to divide 3 by 3 itself, as 3 is the next prime number.

3 ÷ 3 = 1


 We have received 1 at the end and further, we cannot proceed with the division method. So, the prime factors of Forty Eight are 2 × 2 × 2 × 2 × 3 or we can also write them as 2^{4} × 3, where 2 and 3 both are prime numbers.

Examples
Example 1:
Find the common factors of Forty Eight and 47.
Solution:
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
The factors of 47 are 1 and 47.
As 47 is a prime number, the common factor of 47 and 48 is 1.
Example 2:
Find the common factors of Forty Eight and 49.
Solution:
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Factors of 49 = 1, 7, and 49.
Thus, the common factor of 48 and 49 is 1.
Frequently Asked Questions on Factors of Forty Eight
Q1 What are the factors of Forty Eight?
Ans. The factors of Forty Eight are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Q2 What is the prime factorization of Forty Eight?
Ans. The prime factorization of Forty Eight is 2×2×2×2×3 or 2^{4} × 3.
Q3 Write down the positive pair factors of Forty Eight?
Ans. The positive pair factors of Forty Eight are (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8).
Q4 What are the negative pair factors of Forty Eight?
Ans. The negative pair factors of Forty Eight are (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8).
Q5 Is 24 a factor of Forty Eight?
Ans. Yes, 24 is a factor of Forty Eight. If 48 is divided by 24, it leaves a remainder 0, and hence 24 is a factor of Forty Eight.
Category: Maths