 # Factors of 768: Prime Factorization, Methods, and Examples

Numbers which completely divisible by 768 are said to be factors so in this case, the factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, and 768 which give no remainder when divided with 768. ### Factors of 768

Here are the factors of number 768.

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

### Negative Factors of 768

The negative factors of 768 are similar to its positive aspects, just with a negative sign.

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

### Prime Factorization of 768

The prime factorization of 768 is the way of expressing its prime factors in the product form. Prime Factorization: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

In this article, we will learn about the factors of 768 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the 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, and 768. These numbers are the factors as they do not leave any remainder when divided by 768.

The factors of 768 are classified as prime numbers and composite numbers. The prime factors of the number 768 can be determined using the prime factorization technique.

## How To Find the Factors of 768?

You can find the factors of 768 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 768, create a list containing the numbers that are exactly divisible by 768 with zero remainders. One important thing to note is that 1 and 768 are the 768’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 768 are determined as follows:

$\dfrac{768}{1} = 768$

$\dfrac{768}{2} = 384$

$\dfrac{768}{3} = 256$

$\dfrac{768}{4} = 192$

$\dfrac{768}{6} = 128$

$\dfrac{768}{8} = 96$

$\dfrac{768}{12} = 64$

$\dfrac{768}{16} = 48$

$\dfrac{768}{24} = 32$

$\dfrac{768}{768} = 1$

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

### Total Number of Factors of 768

For 768, there are 18 positive factors and 18 negative ones. So in total, there are 36 factors of 768.

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization/prime factorization of the given number.
2. Demonstrate the prime factorization of the number in the form of exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 768 is given as:

Factorization of 768 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 .

The exponent of 2 and 3 is 8,1.

Adding 1 to each and multiplying them together results in 18.

Therefore, the total number of factors of 768 is 32. Eighteen are positive, and eighteen factors are negative.

### Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The factors of the number cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

## Factors of 768 by Prime Factorization

The number 768 is a composite. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 768 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 768, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 768 can be expressed as:

768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

## Factors of 768 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given. For 768, the factor pairs can be found as:

1 x 768 = 768

2 x 384 = 768

3 x 256 = 768

4 x 192 = 768

6 x 128 = 768

8 x 96 = 768

12 x 64 = 768

16 x 48 = 768

24 x 32 = 768

The possible factor pairs of 768 are given as (1, 768), (2, 384),(3, 256), (4, 192), (6, 128), (8, 96 ), (12, 64), (16, 48) and (24, 32).

All these numbers in pairs, when multiplied, give 768 as the product.

The negative factor pairs of 768 are given as:

-1 x -768 = 768

-2 x -384 = 768

-3 x -256 = 768

-4 x -192 = 768

-6 x -128 = 768

-8 x -96 = 768

-12 x -64 = 768

-16 x -48 = 768

-24 x -32 = 768

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -64, -96, -128, -192, -256, -384, and -768 are called negative factors of 768.

The list of all the factors of 768, including positive as well as negative numbers, is given below.

Factor list of 768: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 16, -16, 24, -24, 32, -32, 48, -48, 64, -64, 96, -96, 128, -128, 192, -192, 256, -256, 384, -384, 768 and -768

## Factors of 768 Solved Examples

To better understand the concept of factors, let’s solve some examples.

### Example 1

How many factors of 768 are there?

### Solution

The total number of Factors of 768 is 18.

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

### Example 2

Find the factors of 768 using prime factorization.

### Solution

The prime factorization of 768 is given as:

768 $\div$ 2 = 384

384 $\div$ 2 = 192

192 $\div$ 2 = 96

96 $\div$ 2 = 48

48 $\div$ 2 = 24

24 $\div$ 2 = 12

12 $\div$ 2 = 6

6 $\div$ 2 = 3

3 $\div$ 3 = 1

So the prime factorization of 768 can be written as:

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 768