 # Factors of 760: Prime Factorization, Methods, and Examples

When subtracted from 760, the numbers that leave zero as the final result are referred to as the factors of 760. These numbers also don’t consider the quotient of the total number.

### Factors of 760

Here are the factors of number 760.

Factors of 760: 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380 and 760

### Negative Factors of 760

The negative factors of 760 are similar to its positive aspects, just with a negative sign.

Negative Factors of 760:  -1, -2, -4, -5, -8, -10, -19, -20, -38, -40, -76,- 95,-152, -190, -380 and -760

### Prime Factorization of 760

The prime factorization of 760 is the way of expressing its prime factors in the product form. Prime Factorization: 23 x 51 x 191

In this article, we will learn about the factors of 760 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 760?

The factors of 760 are  1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380 and 760. These numbers are the factors as they do not leave any remainder when divided by 760.

The factors of 760 are classified as prime numbers and composite numbers. The prime factors of the number 760 can be determined using the prime factorization technique.

## How To Find the Factors of 760?

You can find the factors of 760 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 760, create a list containing the numbers that are exactly divisible by 760 with zero remainders. One important thing to note is that 1 and 760 are the 760’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 760 are determined as follows:

$\dfrac{760}{1} = 760$

$\dfrac{760}{2} = 380$

$\dfrac{760}{4} = 190$

$\dfrac{760}{5} = 152$

$\dfrac{760}{8} = 95$

$\dfrac{760}{10} = 76$

$\dfrac{760}{19} = 40$

$\dfrac{760}{20} =38$

$\dfrac{760}{38} = 20$

$\dfrac{760}{40} = 19$

$\dfrac{760}{76} = 10$

$\dfrac{760}{95} = 8$

$\dfrac{760}{152} = 5$

$\dfrac{760}{190} = 4$

$\dfrac{760}{380} = 2$

$\dfrac{760}{760} = 1$

Therefore,  1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380 and 760 are the factors of 760.

### Total Number of Factors of 760

For 760, there are 16 positive factors and 16 negative ones. So in total, there are 32 factors of 760.

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 760 is given as:

Factorization of 760 is 23 x 51 x 191.

The exponent of 2 is 3,  5 is 1, and 19  is 1.

Adding 1 to each and multiplying them together results in 32.

Therefore, the total number of factors of 760 is 32. 16 is positive, and 16 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 760 by Prime Factorization

The number 760 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 760 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 760, 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 760 can be expressed as:

760 = 23 x 51 x 191

## Factors of 760 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 760, the factor pairs can be found as:

1 x 760 = 760

2 x 380 =760

4 x 190 = 760

5 x 152 = 760

8 x 95 = 760

10 x 76 = 760

19 x 40 =760

20 x 38 =760

The possible factor pairs of 760 are given as (1, 760),(4, 190),(4, 190),(5, 152),(8, 95),(10, 76),(19, 40), and (20, 38).

All these numbers in pairs, when multiplied, give 760 as the product.

The negative factor pairs of 760 are given as:

-1 x -760 = 760

-2 x -380 =760

-4 x -190 = 760

-5 x -152 = 760

-8 x -95 = 760

-10 x -76 = 760

-19 x -40 =760

-20 x -38 =760

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, -5, -8, -10, -19, -20, -38, -40, -76,- 95,-152, -190, -380 and -760 are called negative factors of 760.

The list of all the factors of 760, including positive as well as negative numbers, is given below.

Factor list of 760: 1,-1,2, -2, 4,-4, 5,-5,8, -8,10, -10, 19,-19, 20,-20, 38,-38, 40,-40, 76,-76,-95,152,-152, 190,-190, 380,380, 760, and -760

## Factors of 760 Solved Examples

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

### Example 1

How many factors of 760 are there?

### Solution

The total number of Factors of 760 is 32.

Factors of 760 are  1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380 and 760.

### Example 2

Find the factors of 760 using prime factorization.

### Solution

The prime factorization of 760 is given as:

760 $\div$2 =380

380  $\div$ 2= 190

190  $\div$ 2 = 95

95 $\div$ 5 = 19

19 $\div$ 19 = 1

So the prime factorization of 760 can be written as:

23 x 51 x 191 = 760