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Factors of 128 | Prime Factorization of 128 | Factor Tree of 128

Written by Prerit Jain

Updated on: 15 Feb 2023

Factors of 128 | Prime Factorization of 128 | Factor Tree of 128

Factors of 128 | Prime Factorization of 128 | Factor Tree of 128

The factors of a number are the numbers that divide the given number completely and evenly. The factors of a number can be both positive and negative. In this article, you will learn about the factors of 128 using the division method, prime factorization method, and factor tree method.

What Are the Factors of 128?

The factors of the given number 128 are the numbers that can divide the given number thoroughly and evenly without any decimal numbers. A number can have both positive and negative factors. Based on the count of the factors the numbers can be classified into prime numbers and composite numbers. The numbers that have more than two factors are known as composite numbers and the numbers with two or less than two numbers are known as prime numbers. In this case, the number 128 is a composite number as it has more than two factors and they are 1, 2, 4, 8, 16, 32, 64, and 128. 

Factors of 128: 1, 2, 4, 8, 16, 32, 64, and 128. 
Negative Factors of 128: -1, -2, -4, -8, -16, -32, -64, and -128. 
Prime Factorization of 128 are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1
Pair Factors of 128: (1, 128), (2, 64), (4, 32), and (8, 16).
Prime Factors of 128: 2
Sum of Factors of 128: 255
Sum of Prime Factors of 128: 2
Factors of 128

What Are the Factors of 128 in Pairs?

There are both positive and negative factors for a number. A pair factor of a number is a combination of two numbers and on multiplying both numbers, the resultant should always be the given number. In this case, it has to be 128.

Positive Pair Factors of 128

The positive pair factors of 128 are (1, 128), (2, 64), (4, 32), and (8, 16).

Positive Pair Factors of 128

Negative Pair Factors of 128

The negative pair factors of (-1, -128), (-2, -64), (-4, -32), and (-8, -16).

Negative Pair Factors of 128

What Is the Factor Tree of 128?

The prime factors of a number can be identified using the factor tree method. The number for which the prime factors have to be found is placed at the top of the factor tree. Here, it’s 128 and now, split the pair factors of 128 into its branches. And continue this process until the branches become prime factors. In the end, circle the prime factors. The following are the steps given below for a better understanding:

  • Step 1: Let’s place the number 128 at the top of the factor tree and write down the pair factors 2, and 64 in two branches.
  • Step 2: Now, place the pair factors of 64 in the branches and they are 2 and 32.
  • Step 3: 32 has pair factors and so place the pair factors in its branches. They are 2 and 16.
  • Step 4: Again 16 have factors and so place its pair factors in the branches. The pair factors are 2 and 8.
  • Step 5: Now place the pair factors 2 and 4 in the branches of 8.
  • Step 6: Again 8 has 2 and 4 as the pair factors and so place them in its branches.
  • Step 7: Now place the pair factors of 4, 2, and 2 in the branches. And so 2 is a prime number and so we cant further make pair factors for it.

Therefore, the prime factors of 128 are 2 x 2 x 2 x 2 x 2 x 2 x 2. The below image represents the factor tree of 128.

Factor tree of 128

How to Find Factors of 128 Through Division Method?

The long division method is used to find out the factors of a number. Basically, in this method, the given number 128 is divided by a sequence of natural integers. The numbers that divide the given number 128 without any decimal points are known as the factors of 128. Through the steps given below, we can identify the factors of 128.

  • 128 ÷1 = 128
  • 128 ÷ 2 = 64
  • 128 ÷ 4 = 34
  • 128 ÷ 8 = 16
  • 128 ÷ 16 = 8
  • 128 ÷ 32 = 4
  • 128 ÷ 64 = 2
  • 128 ÷ 128 = 1

Therefore, the factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.

What Is the Prime Factorization of 128?

Prime factorization is a method used to identify the prime factors of 128. Before applying the prime factorization method to a number, it’s very important to know whether the given number is a prime number or a composite number. In this case, 128 is a composite number as it has more than two factors and so the prime factors can be found by using this method. The following are the steps involved in it:

  • Step 1: Let’s place the number 128 at the top, and divide it by the smallest number that can divide the given number 128 without any decimals and it is 2.
    128 ÷ 2 = 64
  • Step 2: Now, let’s divide 64 by the number 2.
    64 ÷ 2 = 32
  • Step 3: Now, again let’s divide 32 by 2.
    32 ÷ 2= 16
  • Step 4: Again the quotient 16 is divisible by 2.
    16 ÷ 2 = 8
  • Step 5: The quotient 8 is divisible by 2.
    8 ÷ 2 = 4
  • Step 6: Now divide the quotient number 4 by 2.
    4 ÷ 2 = 2
  • Step 7: Now divide the quotient 2 by 2.
    2 ÷ 2 = 1
  • Step 8: Now let’s circle the prime numbers as the number 1 is not further divisible.

Therefore, the prime factor of 128 is 2. The below image is a visual representation of the prime factorization of 128.

Prime Factorization of 128

Solved Examples of 128

What are the factors of 128?
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128. 

What are the prime factors of 128?
The p[rime factor of 128 is 2.

What is the sum of the factors of 128?
The sum of the factors of 128 is 255.

What are the negative factors of 128?
The negative factors of 128 are -1, -2, -4, -8, -16, -32, -64, and -128. 

Frequently Asked Questions

What two numbers make 128?
The numbers that make 128 are (1, 128), (2, 64), (4, 32), and (8, 16).

Is 128 a prime number?
No, 128 is a composite number, as it has more than 2 factors.

Is 128 a multiple of 3?
No, 128 is not a multiple of 3, as 128 is not divisible by 3.

Is 128 a multiple of 6?
No, 128 is not a multiple of 6, as it’s not divisible by 6.

What are divisible by 128?
All the multiples of 128 are divisible by 128.

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Prerit Jain

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