Factors of 128

Definition of factors of 128: If a number completely divides 128 without leaving a remainder, then that number is called a factor of 128.  In this article, we will learn about the factors of 128 and the prime factors of 128. We have:

  • 128 = 2×2×2×2×2×2×2 = 27 is the prime factorization of 128
  • The factors of 128 are 1, 2, 4, 8, 16, 32, 64 and 128
  • The prime factor of 128 is 2 only.
  • Negative factors of 128 are -1, -2, -4, -8, -16, -32, -64 and -128

What are the factors of 128?

Let us write the number 128 multiplicatively in all possible ways. We definitely have:

128 = 1×128 

128 = 2×64

128 = 4×32

128 = 8×16

As there are no other ways we can write 128 multiplicatively, so we will stop right now. So the factors of 128 in pairs are given as follows:

128 = a×b Factors in Pairs (a,b)
128 = 1×128  (1, 128)
128 = 2×64 (2, 64)
128 = 4×32 (4, 32)
128 = 8×16 (8, 16)

Thus the pair factors of 128 are (1, 128), (2, 64), (4, 32), and (8, 16). As all the numbers appearing in pair factors are the factors of 128, we conclude that

The factors of 128 are:

1, 2, 4, 8, 16, 32, 64 and 128.

Number of factors of 128

From above we have calculated the factors of 128 which are 1, 2, 4, 8, 16, 32, 64, and 128.

Thus the total number of factors of 128 is eight.

Prime Factors of 128

Note that the factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128. Among these factors, we observe that only 2 is a prime number as it does not have any proper divisors.

∴ the only prime factor of 128 is 2.

Question: What are the factors of 128?

Video Solution:

How to find factors of 128?

Now we will determine the factors of 128 by division method. In this method, we will try to find the numbers that can divide 128 with no remainder. See that

128/1=128 and the remainder is 0. 1 and 128 are factors of 128.
128/2=64 and the remainder is 0. 2 and 64 are factors of 128.
128/4=32 and the remainder is 0. 4 and 32 are factors of 128.
128/8=16 and the remainder is 0. 8 and 16 are factors of 128.

Note that no numbers other than the numbers in violet color can divide 128. So the numbers in violet color, that is, 1,2, 4, 8, 16, 32, 64, and 128. are the complete list of factors of 128.

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