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Factors of 128
Do you know, the number 128 has three perfect squares as its factors? These include 4, 16, and 64. In all, it has 8 factors. In this lesson, we will calculate the factors of 128, prime factors of 128, and factors of 128 in pairs along with solved examples for a better understanding.
 Factors of 128: 1, 2, 4, 8, 16, 32, 64, and 128
 Prime Factorization of 128: 128 = 2^{7}
1.  What Are the Factors of 128? 
2.  How to Calculate the Factors of 128? 
3.  Factors of 128 by Prime Factorization 
4.  Factors of 128 in Pairs 
5.  Important Notes 
6.  FAQs on Factors of 128 
What Are the Factors of 128?
The factor of a number is that number which divides the given number completely, i.e., it leaves no remainder. To find the factors of the number 128, we will have to perform division on 128 and find the numbers which divide 128 completely, leaving no remainders.
All the divisors which give remainder 0 for our number 128 are the factors of 128. The diagram below provides the representation of the above definition.
How to Calculate the Factors of 128?
To calculate the factors of any number, here in this case 128, we need to find all the numbers that would divide 128 without leaving any remainder. We start with the number 1, then check for numbers 2, 3, 4, 5, 6, 7, etc. up to 64 (half of 128).
The number 1 and the number itself would always be the factors of the given number. Refer to the following table to check division of 128 by its factors:
Division  Factor 

128/1 
Remainder = 0 Hence, factor = 1 
128/2 
Remainder = 0 Hence, factor = 2 
128/3 
Remainder = 2 3 is not a factor. 
128/4 
Remainder = 0 Hence, factor = 4 
128/8 
Remainder = 0 Hence, factor = 8 
128/16 
Remainder = 0 Hence, factor = 16 
128/32 
Remainder = 0 Hence, factor = 32 
128/64 
Remainder = 0 Hence, factor = 64 
128/128 
Remainder = 0 Hence, factor = 128 
Hence, the factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.
Explore factors using illustrations and interactive examples.
 Factors of 144  The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72,144
 Factors of 65  The factors of 65 are 1, 5, 13, 65
 Factors of 75  The factors of 75 are 1, 3, 5, 15, 25, 75
 Factors of 28  The factors of 28 are 1, 2, 4, 7, 14, 28
 Factors of 72  The factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, 72
 Factors of 250  The factors of 250 are 1, 2, 5, 10, 25, 50, 125, 250
Factors of 128 by Prime Factorization
Prime factorization of a number refers to breaking down a number into the form of products of its prime factors. There are different methods that can be used to find the prime factorization of a number and hence its prime factors.
To find prime factors of 128 using the division method,
 Step1. Start dividing 128 from the smallest prime number, i.e., 2, 3, 5, and so on and find the smallest prime factor of the number.
 Step2. After finding the smallest prime factor of the number 128, i.e. 2, divide 128 by 2 to obtain the quotient (64).
128/2 = 64
 Step3. Repeat step1 with the obtained quotient (64) and continue until you get 1 as the quotient. Again, the prime factor for 64 would be 2.
64/2 = 32
Similarly,
32/2 = 16
16/2 = 8
8/2 = 4
4/2 = 2
2/2 = 1
So, the prime factorization of 128 is:
128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
or
128 = 2^{7}
We can follow the same procedure using the factor tree as shown in the diagram given below:
So, the prime factorization of 128 is:
128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
or
128 = 2^{7}
Further, find the products of the multiplicands in different orders to obtain the composite factors of the number. Thus, the total factors can be written including both the prime and composite numbers together as 1, 2, 4, 8, 16, 32, 64, and 128.
Factors of 128 in Pairs
Pair factors are the factors of a number given in pairs which, when multiplied together, give that original number. The pair factors of 128 would be the two numbers which get multiplied together to result in the value of 128.
The following table represents the calculation of pair factors of 128.
Factor Pair  Pair Factorization 

1 and 128  1 × 128 = 128 
2 and 64  2 × 64 = 128 
4 and 32  4 × 32 = 128 
8 and 16  8 × 16 = 128 
Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 128.
The negative factor pairs of 128 would be ( 1, 128 ), ( 2, 64), ( 8, 16), and ( 4, 32).
Important Notes:
 Only whole numbers and integers can be converted to factors.
 Only composite numbers can have more than two factors.
 The smallest factor of a number is 1 and the biggest factor of a number would be the number itself.
Factors of 128 Solved Examples

Example 1: Sandy is finding the product of all the factors of 128. Can you help her solve it?
Solution:
We know that the factors of 128 = 1, 2, 4, 8, 16, 32, 64, 128
The product of all the factors = 1 × 2 × 4 × 8 × 16 × 32 × 64 × 128 = 268,435,456Hence, the product = 268,435,456

Example 2: Seth is puzzled while calculating the total number of factor pairs of 128. Can you help him find it?
Solution:
We know that the factors of 128 = 1, 2, 4, 8, 16, 32, 64, 128
Positive and negative factor pairs of 128 = (1, 128), (2, 64), (4, 32), (1, 128), (2, 64), (4,32)Hence, total factor pairs of 128 = 6
FAQs on Factors of 128
What are the factors of 128?
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.
Is 128 a perfect square?
We know, 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
On finding square root of 128, we can see that 3 pairs of the same number can be formed, but one number will still remain within square root.
Hence, 128 is not a perfect square.
What are the factors of 128 and 129?
The factor of a number is that number which divides it completely, i.e., it leaves no remainder.
Factors of 128 = 1, 2, 4, 8, 16, 32, 64, 128
Factors of 129 = 1, 3, 43, 129
What is the prime factorization of 128?
Prime factorization of a number refers to breaking down a number into the form of products of its prime factors.
So, the prime factorization of 128 is 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^{7}
What are the common factors of 128 and 45?
Factors of 128 = 1, 2, 4, 8, 16, 32, 64, 128
Factors of 45 = 1, 3, 5, 9, 15, 45
The common factor of 128 and 45 is 1.
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