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# Factors of 682: Prime Factorization, Methods, and Examples

The **factors of 682** are numbers that give a **zero remainder** when divided by 682. 682 is an **even composite** number. This means it has more than two factors.

Its prime factorization with examples is explained in detail in this article.

### Factors of 682

Here are the factors of number** 682.**

**Factors of 682**: 1, 2, 11, 22, 31, 62, 341, and 682

### Negative Factors of 682

The **negative factors of 682 **are similar to its positive aspects, just with a negative sign.

**Negative Factors of 682**: -1, -2, -11, -22, -31, -62, -341, and -682

### Prime Factorization of 682

The **prime factorization of 682 **is the way of expressing its prime factors in the product form.

**Prime Factorization**: 2 x 11 x 31

In this article, we will learn about the **factors of 682 **and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 682?

**The factors of 682 are 1, 2, 11, 22, 31, 62, 341, and 682****. These numbers are the factors as they do not leave any remainder when divided by 682.**

The **factors of 682 **are classified as prime numbers and composite numbers. The prime factors of the number 682 can be determined using the prime factorization technique.

## How To Find the Factors of 682?

You can find the **factors of 682 **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 682, create a list containing the numbers that are exactly divisible by 682 with zero remainders. One important thing to note is that 1 and 682 are the 682’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 682 are determined as follows:

\[\dfrac{682}{1} = 682\]

\[\dfrac{682}{2} = 341\]

\[\dfrac{682}{11} = 62\]

\[\dfrac{682}{22} = 31\]

\[\dfrac{682}{682} = 1\]

Therefore, 1, 2, 11, 22, 31, 62, 341, and 682 are the factors of 682.

### Total Number of Factors of 682

For 682, there are 8 **positive factors** and 8 **negative** ones. So in total, there are 16 factors of 682.

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

- Find the factorization/prime factorization of the given number.
- Demonstrate the prime factorization of the number in the form of exponent form.
- Add 1 to each of the exponents of the prime factor.
- 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 682 is given as:

Factorization of 682 is** 1 x 2 x 11 x 31**.

The exponent of 1, 2, 11, and 31 is 1.

Adding 1 to each and multiplying them together results in 16.

Therefore, the **total number of factors** of 682 is 16. 8 are positive, and 8 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 682 by Prime Factorization

The **number 682 **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 682 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 682, 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 682 **can be expressed as:

**682 = 2 x 11 x 31**

## Factors of 682 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 682, the factor pairs can be found as:

**1 x 682 = 682**

**2 x 341 = 682**

**11 x 62 = 682**

**22 x 31 = 682**

The possible** factor pairs of 682 **are given as **(1, 682), (2, 341), (11, 62), **and **(22, 31)**.

All these numbers in pairs, when multiplied, give 682 as the product.

The **negative factor pairs** of 682 are given as:

**-1 x -682 = 682**

**-2 x -341 = 682**

**-11 x -62 = 682**

**-22 x -31 = 682**

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, -11, -22, -31, -62, -341, and -682 are called negative factors of 682.

The list of all the factors of 682, including positive as well as negative numbers, is given below.

**Factor list of 682: 1, -1, 2, -2, 11, -11, 22, -22, 31, -31, 62, -62, 341, -341, 682, and -682**

## Factors of 682 Solved Examples

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

### Example 1

How many factors of 682 are there?

### Solution

The total number of Factors of 682 is 16.

Factors of 682 are 1, 2, 11, 22, 31, 62, 341, and 682.

### Example 2

Find the factors of 682 using prime factorization.

### Solution

The prime factorization of 682 is given as:

**682 $\div$ 2 = 341 **

**341 $\div$ 11 = 31**

**31 $\div$ 31 = 1 **

So the prime factorization of 682 can be written as:

**1 x 11 x 31 = 682**