# Factors of 32768

Factors of 32768 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, and 32768

#### How to find factors of a number

 1.   Find factors of 32768 using Division Method 2.   Find factors of 32768 using Prime Factorization 3.   Find factors of 32768 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 32768

• Divide 32768 by 1: 32768 ÷ 1 : Remainder = 0
• Divide 32768 by 2: 32768 ÷ 2 : Remainder = 0
• Divide 32768 by 4: 32768 ÷ 4 : Remainder = 0
• Divide 32768 by 8: 32768 ÷ 8 : Remainder = 0
• Divide 32768 by 16: 32768 ÷ 16 : Remainder = 0
• Divide 32768 by 32: 32768 ÷ 32 : Remainder = 0
• Divide 32768 by 64: 32768 ÷ 64 : Remainder = 0
• Divide 32768 by 128: 32768 ÷ 128 : Remainder = 0
• Divide 32768 by 256: 32768 ÷ 256 : Remainder = 0
• Divide 32768 by 512: 32768 ÷ 512 : Remainder = 0
• Divide 32768 by 1024: 32768 ÷ 1024 : Remainder = 0
• Divide 32768 by 2048: 32768 ÷ 2048 : Remainder = 0
• Divide 32768 by 4096: 32768 ÷ 4096 : Remainder = 0
• Divide 32768 by 8192: 32768 ÷ 8192 : Remainder = 0
• Divide 32768 by 16384: 32768 ÷ 16384 : Remainder = 0
• Divide 32768 by 32768: 32768 ÷ 32768 : Remainder = 0

Hence, Factors of 32768 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, and 32768

#### 2. Steps to find factors of 32768 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 32768 using the division method, follow these steps:

• Step 1. Start dividing 32768 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 32768, which is 2. Divide 32768 by 2 to obtain the quotient (16384).
32768 ÷ 2 = 16384
• Step 3. Repeat step 1 with the obtained quotient (16384).
16384 ÷ 2 = 8192
8192 ÷ 2 = 4096
4096 ÷ 2 = 2048
2048 ÷ 2 = 1024
1024 ÷ 2 = 512
512 ÷ 2 = 256
256 ÷ 2 = 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 32768 is, 32768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 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 32768 as shown below:

So, the prime factorization of 32768 is, 32768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.

#### 3. Find factors of 32768 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 32768 would be the two numbers which, when multiplied, give 32768 as the result.

The following table represents the calculation of factors of 32768 in pairs:

Factor Pair Pair Factorization
1 and 32768 1 x 32768 = 32768
2 and 16384 2 x 16384 = 32768
4 and 8192 4 x 8192 = 32768
8 and 4096 8 x 4096 = 32768
16 and 2048 16 x 2048 = 32768
32 and 1024 32 x 1024 = 32768
64 and 512 64 x 512 = 32768
128 and 256 128 x 256 = 32768

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 32768. They are called negative pair factors.

Hence, the negative pairs of 32768 would be ( -1 , -32768 ) , ( -2 , -16384 ) , ( -4 , -8192 ) , ( -8 , -4096 ) , ( -16 , -2048 ) , ( -32 , -1024 ) , ( -64 , -512 ) and ( -128 , -256 ) .

#### 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. 32768 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 32768.
• Every number is a factor of zero (0), since 32768 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, 512, 1024, 2048, 4096, 8192, 16384, 32768 are exact divisors of 32768.
• Factors of 32768 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768. Each factor divides 32768 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, 512, 1024, 2048, 4096, 8192, 16384, 32768 are all less than or equal to 32768.

• What is prime factorization of 32768?

Prime factorization of 32768 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.

• How do you find factors of a negative number? ( eg. -32768 )?

Factors of -32768 are -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, -32768.

• What are the prime factors of 32768?

The factors of 32768 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768.
Prime factors of 32768 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2.

• What are pair factors of 32768?

The pair factors of 32768 are (1,32768), (2,16384), (4,8192), (8,4096), (16,2048), (32,1024), (64,512), (128,256).

• What is the greatest prime factors of 32768?

The greatest prime factor of 32768 is 2.

• What are six multiples of 32768?

First five multiples of 32768 are 65536, 98304, 131072, 163840, 196608, 229376.

• What are factors of 32768?

Factors of 32768 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768.

• Which is the smallest prime factor of 32768?

Smallest prime factor of 32768 is 2.

• Is 32768 a whole number?

Yes 32768 is a whole number.

#### Examples of Factors

Kevin has been asked to write 15 factor(s) of 32768. Can you predict the answer?

15 factor(s) of 32768 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384.

Sammy is puzzled while calculating the prime factors of 32768. Can you help him find them?

Factors of 32768 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768.
Prime factors of 32768 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

What is prime factorization of 32768?

Prime factorization of 32768 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 215.

Ariel has been assigned the task to find the product of all the prime factors of 32768. Can you help her?

Prime factors of 32768 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2.
Hence, the product of prime factors of 2.

Can you help Rubel to find out the product of the even factors of 32768?

Factors of 32768 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768.
Even factors of 32768 are 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768.
Hence, product of even factors of 32768 is; 2 x 4 x 8 x 16 x 32 x 64 x 128 x 256 x 512 x 1024 x 2048 x 4096 x 8192 x 16384 x 32768 = 1.329227995784916e+36.

Joy wants to calculate mean of all the factors of 32768. Help him in finding the mean of 32768.

Factors of 32768 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 32768 is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096 + 8192 + 16384 + 32768 = 65535.
Hence, the mean of factors of 32768 is 65535 ÷ 16 = 4095.94.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 32768? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768.
Negative factors are -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024, -2048, -4096, -8192, -16384, -32768.