# Factors of 768

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

#### How to find factors of a number

 1.   Find factors of 768 using Division Method 2.   Find factors of 768 using Prime Factorization 3.   Find factors of 768 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 768

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

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

#### 2. Steps to find factors of 768 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 768 using the division method, follow these steps:

• Step 1. Start dividing 768 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 768, which is 2. Divide 768 by 2 to obtain the quotient (384).
768 ÷ 2 = 384
• Step 3. Repeat step 1 with the obtained quotient (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 768 is, 768 = 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 768 as shown below:

So, the prime factorization of 768 is, 768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3.

#### 3. Find factors of 768 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 768 would be the two numbers which, when multiplied, give 768 as the result.

The following table represents the calculation of factors of 768 in pairs:

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

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 768. They are called negative pair factors.

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

#### 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. 768 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 768.
• Every number is a factor of zero (0), since 768 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, 768 are exact divisors of 768.
• Factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768. Each factor divides 768 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, 768 are all less than or equal to 768.

• What are the prime factors of 768?

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

• What two numbers make 768?

Two numbers that make 768 are 2 and 384.

• What is the greatest prime factors of 768?

The greatest prime factor of 768 is 3.

• What are factors of 768?

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

• How do you find factors of a negative number? ( eg. -768 )?

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

• What are five multiples of 768?

First five multiples of 768 are 1536, 2304, 3072, 3840, 4608.

• Write some multiples of 768?

First five multiples of 768 are 1536, 2304, 3072, 3840.

• Is 768 a perfect square?

No 768 is not a perfect square.

• What two numbers make 768?

Two numbers that make 768 are 2 and 384.

#### Examples of Factors

What is prime factorization of 768?

Prime factorization of 768 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 28 x 3.

Sammy is puzzled while calculating the prime factors of 768. Can you help him find them?

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

Kevin has been asked to write 17 factor(s) of 768. Can you predict the answer?

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

Joey wants to write all the prime factors of 768 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 768 are 2, 2, 2, 2, 2, 2, 2, 2, 3.
So in exponential form it can be written as 28 x 3.

How many factors are there for 768?

Factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768.
So there are in total 18 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 768? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768.
Negative factors are -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -64, -96, -128, -192, -256, -384, -768.

Can you help Rubel to find out the product of the even factors of 768?

Factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768.
Even factors of 768 are 2, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768.
Hence, product of even factors of 768 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 768 = 3.0983446494107742e+25.