Factors of 256

The factors of 256 are the numbers that divide 256 completely without leaving any remainder. The pair factors of 256 can be represented in positive and negative forms. For example, the pair factor of 256 is expressed as (1, 256) or (-1, -256). If we multiply -1 and -256, it will result in the original number 256. Here, we will learn the factors of 256, positive and negative pair factors of 256, how to find the prime factors of 256 using the prime factorization method and many solved examples.

Table of Contents:

• What Are The Factors Of 256?
• Pair Factors Of 256
• Factors Of 256 By Division Method
• Prime Factorization Of 256
• Solved Examples
• FAQs

What are the Factors of 256?

In Mathematics, the factors of a number are the numbers that divide the given number exactly without leaving any remainder. Thus, the factors of 256 are the numbers that divide 256 evenly and leave the remainder value 0. Thus, the factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128 and 256. Similarly, the negative factors of 256 are -1, -2, -4, -8, -16, -32, -64, -128 and -256.

Pair Factors of 256

A pair of numbers that are multiplied together resulting in the original number 256, is the pair factor of 256. As the number 256 is an even composite number, it has more than one pair factor. Thus, the positive and negative pair factors of 256 are as follows:

Positive Pair Factors of 256:

Therefore, the positive pair factors of 256 are (1, 256), (2, 128), (4, 64), (8, 32) and (16, 16).

Negative Pair Factors of 256:

Therefore, the negative pair factors of 256 are (-1, -256), (-2, -128), (-4, -64), (-8, -32) and (-16, -16).

Factors of 256 by Division Method

In the division method, the factors of 256 are determined by dividing the number 256 by different integer numbers. If the integer divides 256 completely, then the integer is a factor of 256. Go through the following procedure to find the factors of 256 using the division method.

• 256/1 = 256 (Factor is 1 and Remainder is 0)
• 256/2 = 128 (Factor is 2 and Remainder is 0)
• 256/4 = 64 (Factor is 4 and Remainder is 0)
• 256/8 = 32 (Factor is 8 and Remainder is 0)
• 256/16 = 16 (Factor is 16 and Remainder is 0)
• 256/32 = 8 (Factor is 32 and Remainder is 0)
• 256/64 = 4 (Factor is 64 and Remainder is 0)
• 256/128 = 2 (Factor is 128 and Remainder is 0)
• 256/256 = 1 (Factor is 256 and Remainder is 0)

Therefore, the factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128 and 256.

Note: If we divide 256 by any numbers other than 1, 2, 4, 8, 16, 32, 64, 128 and 256, it leaves a remainder of some integer number.

Prime Factorization of 256

In the prime factorization of 256, the number 256 is written as the product of the prime factors of 256. Thus, the process of finding the prime factors of 256 using the prime factorization method is given below.

Consider a pair factor of 256, say (1, 256)

Now, find two numbers which, on multiplication, result in the original number 256.

Thus, 256 is written as the product of 16 and 16. But still, 16 is a composite number, which can be further split into its prime factors.

We know that 16 is written as 2 × 2 × 2 × 2, where 2 is a prime number.

Therefore,

256 = 16 × 16

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.

Therefore, the prime factorization of 256 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 or 2⁸.

Video Lesson on Prime Factors

Solved Examples

Example 1:

Find the common factors of 256 and 255.

Solution:

The factors of the number 256 are 1, 2, 4, 8, 16, 32, 64, 128 and 256.

The factors of the number 255 are 1, 3, 5, 15, 17, 51, 85 and 255.

Thus, the common factor of 256 and 255 is 1.

Example 2:

Find the common factors of 256 and 257.

Solution:

Factors of 256 = 1, 2, 4, 8, 16, 32, 64, 128 and 256.

Factors of 257 = 1 and 257.

As the number 257 is a prime number, the common factor of 256 and 257 is 1.

Example 3:

What are the common factors of 256 and 32?

Solution:

The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128 and 256.

The factors of 32 are 1, 2, 4, 8, 16 and 32.

Therefore, the common factors of 256 and 32 are 1, 2, 4, 8, 16 and 32.

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