 # Factors of 796: Prime Factorization, Methods, and Examples

The factors of 796 are numbers that, when divided by 796, leave nothing as a remainder. The number 796 is divisible by 1, 2, 4, 199, 398, and itself. The factors of 796 can be positive and negative. In this lesson, we will discuss how to find the factors using the division method.

### Factors of 796

Here are the factors of number 796.

Factors of 796: 1, 2, 4, 199, 398, and 796

### Negative Factors of 796

The negative factors of 796 are similar to their positive aspects, just with a negative sign.

Negative Factors of 796: -1, -2, -4, -199, -398, and -796

### Prime Factorization of 796

The prime factorization of 796 is the way of expressing its prime factors in the product form. Prime Factorization: 2 x 2 x 199

In this article, we will learn about the factors of 796 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 796?

The factors of 796 are 1, 2, 4, 199, 398, and 796. These numbers are the factors as they do not leave any remainder when divided by 796.

The factors of 796 are classified as prime numbers and composite numbers. The prime factors of the number 796 can be determined using the prime factorization technique.

## How To Find the Factors of 796?

You can find the factors of 796 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 796, create a list containing the numbers that are exactly divisible by 796 with zero remainders. One important thing to note is that 1 and 796 are 796’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 796 are determined as follows:

$\dfrac{796}{1} = 796$

$\dfrac{796}{2} = 398$

$\dfrac{796}{4} = 199$

Therefore, 1, 2, 4, 199, 398, and 796 are the factors of 796.

### Total Number of Factors of 796

For 796, there are six positive factors and six negative ones. So in total, there are twelve factors of 796.

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 796 is given as follows:

The factorization of 796 is 1 x 2 x 2 x 199 = 1 x 2$\mathsf{\boldsymbol2}$ x 199

The exponent of 1 and 199 is 1, while the exponent of 2 is 2.

Adding 1 to each and multiplying them together: (1 + 1) x (2 + 1) x (1 + 1) = 12.

Therefore, the total number of factors of 796 is 12. Six are positive, and six 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 796 by Prime Factorization

The number 796 is a prime number. 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 796 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 796, divide 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 796 can be expressed as:

796 = 2 x 2 x 199

## Factors of 796 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 796, the factor pairs can be found as follows:

1 x 796 = 796

2 x 398 = 796

4 x 199 = 796

The possible factor pairs of 796 are given as (1, 796), (2, 398), and (4, 199).

All these numbers in pairs, when multiplied, give 796 as the product.

The negative factor pairs of 796 are given as:

-1 x -796 = 796

-2 x -398 = 796

-4 x -199 = 796

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, -4, -199, -398, and -796 are called negative factors of 796.

The list of all the factors of 796, including positive as well as negative numbers, is given below.

Factor list of 796: 1, -1, 2, -2, 4, -4, 199, -199, 398, -398, 796, and -796

## Factors of 796 Solved Examples

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

### Example 1

How many factors of 796 are there?

### Solution

The total number of Factors of 796 is twelve.

Factors of 796 are 1, 2, 4, 199, 398, and 796.

### Example 2

Find the factors of 796 using prime factorization.

### Solution

The prime factorization of 796 is given as:

796 $\div$ 2 = 398

Since 398 is an even number, we divide again by 2:

398 $\div$ 2 = 199

199 is a prime number, so it is only divisible by itself:

199 $\div$ 199 = 1

So the prime factorization of 796 can be written as:

2 x 2 x 199= 796