# Factors of 1536

Factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, and 1536

#### How to find factors of a number

 1.   Find factors of 1536 using Division Method 2.   Find factors of 1536 using Prime Factorization 3.   Find factors of 1536 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1536

• Divide 1536 by 1: 1536 ÷ 1 : Remainder = 0
• Divide 1536 by 2: 1536 ÷ 2 : Remainder = 0
• Divide 1536 by 3: 1536 ÷ 3 : Remainder = 0
• Divide 1536 by 4: 1536 ÷ 4 : Remainder = 0
• Divide 1536 by 6: 1536 ÷ 6 : Remainder = 0
• Divide 1536 by 8: 1536 ÷ 8 : Remainder = 0
• Divide 1536 by 12: 1536 ÷ 12 : Remainder = 0
• Divide 1536 by 16: 1536 ÷ 16 : Remainder = 0
• Divide 1536 by 24: 1536 ÷ 24 : Remainder = 0
• Divide 1536 by 32: 1536 ÷ 32 : Remainder = 0
• Divide 1536 by 48: 1536 ÷ 48 : Remainder = 0
• Divide 1536 by 64: 1536 ÷ 64 : Remainder = 0
• Divide 1536 by 96: 1536 ÷ 96 : Remainder = 0
• Divide 1536 by 128: 1536 ÷ 128 : Remainder = 0
• Divide 1536 by 192: 1536 ÷ 192 : Remainder = 0
• Divide 1536 by 256: 1536 ÷ 256 : Remainder = 0
• Divide 1536 by 384: 1536 ÷ 384 : Remainder = 0
• Divide 1536 by 512: 1536 ÷ 512 : Remainder = 0
• Divide 1536 by 768: 1536 ÷ 768 : Remainder = 0
• Divide 1536 by 1536: 1536 ÷ 1536 : Remainder = 0

Hence, Factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, and 1536

#### 2. Steps to find factors of 1536 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 1536 using the division method, follow these steps:

• Step 1. Start dividing 1536 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 1536, which is 2. Divide 1536 by 2 to obtain the quotient (768).
1536 ÷ 2 = 768
• Step 3. Repeat step 1 with the obtained quotient (768).
768 ÷ 2 = 384
384 ÷ 2 = 192
192 ÷ 2 = 96
96 ÷ 2 = 48
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1

So, the prime factorization of 1536 is, 1536 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1536 as shown below:

So, the prime factorization of 1536 is, 1536 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3.

#### 3. Find factors of 1536 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 1536 would be the two numbers which, when multiplied, give 1536 as the result.

The following table represents the calculation of factors of 1536 in pairs:

Factor Pair Pair Factorization
1 and 1536 1 x 1536 = 1536
2 and 768 2 x 768 = 1536
3 and 512 3 x 512 = 1536
4 and 384 4 x 384 = 1536
6 and 256 6 x 256 = 1536
8 and 192 8 x 192 = 1536
12 and 128 12 x 128 = 1536
16 and 96 16 x 96 = 1536
24 and 64 24 x 64 = 1536
32 and 48 32 x 48 = 1536

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 1536. They are called negative pair factors.

Hence, the negative pairs of 1536 would be ( -1 , -1536 ) , ( -2 , -768 ) , ( -3 , -512 ) , ( -4 , -384 ) , ( -6 , -256 ) , ( -8 , -192 ) , ( -12 , -128 ) , ( -16 , -96 ) , ( -24 , -64 ) and ( -32 , -48 ) .

#### 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. 1536 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1536.
• Every number is a factor of zero (0), since 1536 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, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536 are exact divisors of 1536.
• Factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536. Each factor divides 1536 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536 are all less than or equal to 1536.

• How do you find factors of a negative number? ( eg. -1536 )?

Factors of -1536 are -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -64, -96, -128, -192, -256, -384, -512, -768, -1536.

• What is the sum of all factors of 1536?

The sum of all factors of 1536 is 4092.

• What is prime factorization of 1536?

Prime factorization of 1536 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3.

• What are the pair factors of 1536?

Pair factors of 1536 are (1,1536), (2,768), (3,512), (4,384), (6,256), (8,192), (12,128), (16,96), (24,64), (32,48).

• What are six multiples of 1536?

First five multiples of 1536 are 3072, 4608, 6144, 7680, 9216, 10752.

• Is 1536 a whole number?

Yes 1536 is a whole number.

• Which is the smallest prime factor of 1536?

Smallest prime factor of 1536 is 2.

• What are five multiples of 1536?

First five multiples of 1536 are 3072, 4608, 6144, 7680, 9216.

• Write all factors of 1536?

Factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536.

#### Examples of Factors

Joey wants to write all the prime factors of 1536 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1536 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 3.
So in exponential form it can be written as 29 x 3.

How many factors are there for 1536?

Factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536.
So there are in total 20 factors.

Kevin has been asked to write 19 factor(s) of 1536. Can you predict the answer?

19 factor(s) of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768.

Sammy is puzzled while calculating the prime factors of 1536. Can you help him find them?

Factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536.
Prime factors of 1536 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 3

What is prime factorization of 1536?

Prime factorization of 1536 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 29 x 3.

Ariel has been assigned the task to find the product of all the prime factors of 1536. Can you help her?

Prime factors of 1536 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 1536?

Factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536.
Even factors of 1536 are 2, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536.
Hence, product of even factors of 1536 is; 2 x 4 x 6 x 8 x 12 x 16 x 24 x 32 x 48 x 64 x 96 x 128 x 192 x 256 x 384 x 512 x 768 x 1536 = 2.436637379325414e+31.