Factors of 256 Using Prime Factorization
What are the Factors of 256?
The factors of any number are numbers that divide a given number with zero as a remainder. Similarly, the factors of 256 are such numbers that divide 256 with a whole number as the quotient. This whole number obtained as the quotient is also a factor of 256.
Hence, we can list the factors of 256 as, 1, 2, 4, 8, 16, 32, 64, 128, and 256.
What are the Factor Pairs of 256?
A factor pair of 256 or any other natural number can be defined as a pair of factors of 256 that when multiplied together result in 256 as the product. In this case we can also observe that 256 is an even composite number with more than one factor pair.
Factor List of 256
We can divide 256 with a set of natural numbers, and if there aren’t any remainders, then, the integers are factors of 256. While creating this factor list, it is to be noted that divisibility rules as well as division facts are applied to find the factors.
Divisor | Is the number a factor of 256? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 256 = 256 |
2 | 2 is a factor as 256 is an even number | 2 x 128 = 256 |
3 | No, 2 + 5 + 6 = 13 is not divisible by 3 | - |
4 | Yes, 256 \(\div\) 4 = 64 R0 | 4 x 64 = 256 |
5 | No, the ones digit is not 5 or 0 | - |
6 | No, Though 256 is even, it is not divisible by 3 | - |
7 | No, 256 ÷ 7 = 36 R4 | - |
8 | Yes, 256 ÷ 8 = 32 R0 | 8 x 32 = 256 |
9 | No, 256 ÷ 9 = 28 R4 | - |
10 | No, the ones digit is not 0 | - |
11 | No, 256 ÷ 11 = 23 R3 | - |
12 | No, 256 ÷ 12 = 21 R4 | - |
13 | No, 256 ÷ 13 = 19 R9 | - |
14 | No, 256 ÷ 14 = 18 R4 | - |
15 | No, 256 ÷ 15 = 17 R1 | - |
16 | Yes, 256 ÷ 16 = 16 R0 | 16 x 16 = 256 |
So, the factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, and 256.
Prime Factorization of 256
When a natural number is expressed as a product of its prime factors, this process is called prime factorization. These prime numbers are called the prime factors of that particular natural number.
The prime factorization of 256 can be expressed as a factor tree as shown in the image.
Hence, the prime factorization of 256 is, 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 or \(2^8\).
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Rapid Recall
The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, and 256.
Solved Factors of 256 Examples
Example 1: Find the common factors of 256 and 160.
Solution:
The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, and 256.
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, and 160.
As a result, the common factors of 256 and 160 are 1, 2, 4, 8, 16 and 32.
Example 2: What is the sum of the factors of 256?
Solution:
The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, and 256.
The sum of these factors = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 = 511.
The sum of the factors is 511.
Example 3: A team of 8 students will distribute 256 cookies in a neighborhood. Later on, two more teams of students join the distribution drive in which one team has 16 students and the other team has 4 students. Each team distributes 256 cookies. How many cookies did each student distribute?
Solution:
As we know, there are a total of three teams with 8, 16, 4 students in each team respectively. Each team distributes 256 cookies. In order to find out the number of cookies each student distributes, we will write down the factor pairs of 256.
(1, 256)
(2, 128)
(4, 64)
(8, 32)
(16, 16)
From the above list of factor pairs, we will take into account the following pairs:
8 x 32 = 256
16 x 16 = 256
4 x 64 = 256
So, in the team of 8 students, each student will distribute 32 cookies. Similarly, in the team of 16 students, each student will distribute 16 cookies and in the team of 4 students, each student will distribute 64 cookies.
Factors of any number are natural numbers that divide it completely without resulting in a remainder.
The prime factorization of 256 is, 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 or \(2^8\).
22 is not a factor of 256 as it cannot divide 256 completely. There will be a remainder of 14, when 256 is divided by 22.
The positive factor pairs of 256 are (1, 256), (2, 128), (4, 64), (8, 32), and (16, 16).