 # Factors of 763: Prime Factorization, Methods, and Examples

The factors of 763 are the numbers that divide it exactly while leaving zero as the unaltered outcome. Apart from that, these divisors produce a quotient of whole numbers. Both these divisors and whole number quotients are referred to as factors.

### Factors of 763

Here are the factors of number 763.

Factors of 763: 1, 7, 109, and 763

### Negative Factors of 763

The negative factors of 763 are similar to their positive aspects, just with a negative sign.

Negative Factors of 763: -1, -7, -109, and -763

### Prime Factorization of 763

The prime factorization of 763 is the way of expressing its prime factors in the product form. Prime Factorization: 7 x 109

In this article, we will learn about the factors of 763 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 763?

The factors of 763 are 1, 7, 109, and 763. These numbers are the factors as they do not leave any remainder when divided by 763.

The factors of 763 are classified as prime numbers and composite numbers. The prime factors of the number 763 can be determined using the prime factorization technique.

## How To Find the Factors of 763?

You can find the factors of 763 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 763, create a list containing the numbers that are exactly divisible by 763 with zero remainders. One important thing to note is that 1 and 763 are the 763’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 763 are determined as follows:

$\dfrac{763}{1} = 763$

$\dfrac{763}{7} = 109$

$\dfrac{763}{109} = 7$

$\dfrac{763}{763} = 1$

Therefore, 1, 7, 109, and 763 are the factors of 763.

### Total Number of Factors of 763

For 763, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 763.

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 763 is given as:

Factorization of 763 is 1 x 7 x 109.

The exponent of 1, 7, and 109 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 763 is 8. 4 are positive, and 4 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 763 by Prime Factorization

The number 763 is a composite 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 763 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 763, 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 763 can be expressed as:

763= 7 x 109

## Factors of 763 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 763, the factor pairs can be found as:

1 x 763 = 763

7 x 109  = 763

The possible factor pairs of 763 are given as (1, 763) and (7, 109).

All these numbers in pairs, when multiplied, give 763 as the product.

The negative factor pairs of 763 are given as:

-1 x -763 = 763

-7 x -109  = 763

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, -7, -109, and -763 are called negative factors of 763.

The list of all the factors of 763, including positive as well as negative numbers, is given below.

Factor list of 763:-1,1, 7,-7, 109,-109,  763, and -763

## Factors of 763 Solved Examples

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

### Example 1

How many factors of 763 are there?

### Solution

The total number of Factors of 763 is 8.

Factors of 763 are 1, 7, 109, and 763.

### Example 2

Find the factors of 763 using prime factorization.

### Solution

The prime factorization of 763 is given as:

763 $\div$ 7 = 109

109$\div$ 109 = 1

So the prime factorization of 763can be written as:

7 x 109  = 763