# Factors of 128

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

#### How to find factors of a number

 1.   Find factors of 128 using Division Method 2.   Find factors of 128 using Prime Factorization 3.   Find factors of 128 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 128

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

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

#### 2. Steps to find factors of 128 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 128 using the division method, follow these steps:

• Step 1. Start dividing 128 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 128, which is 2. Divide 128 by 2 to obtain the quotient (64).
128 ÷ 2 = 64
• Step 3. Repeat step 1 with the obtained quotient (64).
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1

So, the prime factorization of 128 is, 128 = 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 128 as shown below:

So, the prime factorization of 128 is, 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2.

#### 3. Find factors of 128 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 128 would be the two numbers which, when multiplied, give 128 as the result.

The following table represents the calculation of factors of 128 in pairs:

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

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 128. They are called negative pair factors.

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

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 128 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 128.
• Every number is a factor of zero (0), since 128 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 are exact divisors of 128.
• Factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128. Each factor divides 128 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 are all less than or equal to 128.

• What two numbers make 128?

Two numbers that make 128 are 2 and 64.

• What is prime factorization of 128?

Prime factorization of 128 is 2 x 2 x 2 x 2 x 2 x 2 x 2.

• Write some multiples of 128?

First five multiples of 128 are 256, 384, 512, 640.

• Which is the smallest prime factor of 128?

The smallest prime factor of 128 is 2.

• Is 128 a perfect square?

No 128 is not a perfect square.

• What is the sum of all factors of 128?

The sum of all factors of 128 is 255.

• What are factors of 128?

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

• How do you find factors of a negative number? ( eg. -128 )?

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

• Is 128 a whole number?

Yes 128 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 128. Help him in finding the mean of 128.

Factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 128 is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255.
Hence, the mean of factors of 128 is 255 ÷ 8 = 31.88.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 128? Help her in writing all the factors.

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

Joey wants to write all the prime factors of 128 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 128 are 2, 2, 2, 2, 2, 2, 2.
So in exponential form it can be written as 27.

Kevin has been asked to write 7 factor(s) of 128. Can you predict the answer?

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

Sammy is puzzled while calculating the prime factors of 128. Can you help him find them?

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

What is prime factorization of 128?

Prime factorization of 128 is 2 x 2 x 2 x 2 x 2 x 2 x 2 = 27.

Can you help Rubel to find out the product of the even factors of 128?

Factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128.
Even factors of 128 are 2, 4, 8, 16, 32, 64, 128.
Hence, product of even factors of 128 is; 2 x 4 x 8 x 16 x 32 x 64 x 128 = 268435456.