 # Factors of 771: Prime Factorization, Methods, and Examples

The number 771 is an odd composite number with 4 factors and two-factor pairs. The prime factorization is the product of prime factors of the number to get the result equal to the number itself. In the case of 771, the prime factorization is 3 x 257. Further details are provided in the article.

### Factors of 771

Here are the factors of number 771.

Factors of 711: 1, 3, 257, and 771.

### Negative Factors of 771

The negative factors of 771 are similar to its positive aspects, just with a negative sign.

Negative Factors of 771: -1, -3, -257, and -771.

### Prime Factorization of 771

The prime factorization of 771 is the way of expressing its prime factors in the product form. Prime Factorization: 3 x 257

In this article, we will learn about the factors of 771 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 771?

The factors of 771 are 1, 3, 257, and 771. These numbers are the factors as they do not leave any remainder when divided by 771.

The factors of 771 are classified as prime numbers and composite numbers. The prime factors of the number 771 can be determined using the prime factorization technique.

## How To Find the Factors of 771?

You can find the factors of 771 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 771, create a list containing the numbers that are exactly divisible by 771 with zero remainders. One important thing to note is that 1 and 771 are the 771’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 771 are determined as follows:

$\dfrac{771}{1} = 771$

$\dfrac{771}{3} = 257$

$\dfrac{771}{257} = 3$

$\dfrac{771}{771} = 1$

Therefore, 1, 3, 257, and 771 are the factors of 771.

### Total Number of Factors of 771

For 771, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 771.

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 771 is given as:

Factorization of 771 is 1 x 3 x 257.

The exponent of 1, 3, and 257 is 1.

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

Therefore, the total number of factors of 771 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 771 by Prime Factorization

The number 771 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 771 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 771, 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 771 can be expressed as:

771 = 2 x 257

## Factors of 771 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 771, the factor pairs can be found as:

1 x 771 = 771

3 x 257 = 771

The possible factor pairs of 771 are given as (1, 771) and (3, 257).

All these numbers in pairs, when multiplied, give 771 as the product.

The negative factor pairs of 771 are given as:

-1 x -771 = 771

-3 x -257= 771

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, -3, -257, and -771. are called negative factors of 771.

The list of all the factors of 771, including positive as well as negative numbers, is given below.

Factor list of 771: 1, -1, 3, -3, 257, -257, 771, and -771.

## Factors of 771 Solved Examples

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

### Example 1

How many factors of 771 are there?

### Solution

The total number of Factors of 771 is 4.

Factors of 771 are 1, 3, 257, and 771.

### Example 2

Find the factors of 771 using prime factorization.

### Solution

The prime factorization of 771 is given as:

771 $\div$ 3 = 257

257 $\div$ 257 = 1

So the prime factorization of 771 can be written as:

3 x 257 = 771