# Factors of 256

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

#### How to find factors of a number

 1.   Find factors of 256 using Division Method 2.   Find factors of 256 using Prime Factorization 3.   Find factors of 256 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 256

• Divide 256 by 1: 256 ÷ 1 : Remainder = 0
• Divide 256 by 2: 256 ÷ 2 : Remainder = 0
• Divide 256 by 4: 256 ÷ 4 : Remainder = 0
• Divide 256 by 8: 256 ÷ 8 : Remainder = 0
• Divide 256 by 16: 256 ÷ 16 : Remainder = 0
• Divide 256 by 32: 256 ÷ 32 : Remainder = 0
• Divide 256 by 64: 256 ÷ 64 : Remainder = 0
• Divide 256 by 128: 256 ÷ 128 : Remainder = 0
• Divide 256 by 256: 256 ÷ 256 : Remainder = 0

Hence, Factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, and 256

#### 2. Steps to find factors of 256 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 256 using the division method, follow these steps:

• Step 1. Start dividing 256 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 256, which is 2. Divide 256 by 2 to obtain the quotient (128).
256 ÷ 2 = 128
• Step 3. Repeat step 1 with the obtained quotient (128).
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1

So, the prime factorization of 256 is, 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 256 as shown below:

So, the prime factorization of 256 is, 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.

#### 3. Find factors of 256 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 256 would be the two numbers which, when multiplied, give 256 as the result.

The following table represents the calculation of factors of 256 in pairs:

Factor Pair Pair Factorization
1 and 256 1 x 256 = 256
2 and 128 2 x 128 = 256
4 and 64 4 x 64 = 256
8 and 32 8 x 32 = 256
16 and 16 16 x 16 = 256

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 256. They are called negative pair factors.

Hence, the negative pairs of 256 would be ( -1 , -256 ) , ( -2 , -128 ) , ( -4 , -64 ) , ( -8 , -32 ) and ( -16 , -16 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 256 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 256.
• Every number is a factor of zero (0), since 256 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 8, 16, 32, 64, 128, 256 are exact divisors of 256.
• Factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256. Each factor divides 256 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 32, 64, 128, 256 are all less than or equal to 256.

• Is 256 a perfect square?

Yes 256 is a perfect square.

• What are factors of 256?

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

• Which is greatest factor of 256?

The greatest factor of 256 is 128.

• What is the sum of all factors of 256?

The sum of all factors of 256 is 511.

• What are multiples of 256?

First five multiples of 256 are 512, 768, 1024, 1280.

• What is the greatest prime factors of 256?

The greatest prime factor of 256 is 2.

• What are six multiples of 256?

First five multiples of 256 are 512, 768, 1024, 1280, 1536, 1792.

• What is prime factorization of 256?

Prime factorization of 256 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.

• Is 256 a whole number?

Yes 256 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 256? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 16, 32, 64, 128, 256.
Negative factors are -1, -2, -4, -8, -16, -32, -64, -128, -256.

Can you help Sammy find out the product of the odd factors of 256?

Factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256.
Odd factors of 256 are 1.
Hence product of odd factors of 256 is; 1 = 1.

Joey wants to write all the prime factors of 256 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 256 are 2, 2, 2, 2, 2, 2, 2, 2.
So in exponential form it can be written as 28.

How many factors are there for 256?

Factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256.
So there are in total 9 factors.

Kevin has been asked to write 8 factor(s) of 256. Can you predict the answer?

8 factor(s) of 256 are 1, 2, 4, 8, 16, 32, 64, 128.

Sammy is puzzled while calculating the prime factors of 256. Can you help him find them?

Factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256.
Prime factors of 256 are 2, 2, 2, 2, 2, 2, 2, 2

What is prime factorization of 256?

Prime factorization of 256 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 28.