# Factors of 685: Prime Factorization, Methods, and Examples

The natural numbers that, when added together, provide the number 685 are the factors of 685. 4 components make up all of 685.Â

These variables may be either positive or negative as long as they multiply two integer variables to produce the provided value.

### Factors of 685

Here are the factors of number 685.

Factors of 685: 1, 5, 137, 685

### Negative Factors of 685

The negative factors of 685 are similar to their positive aspects, just with a negative sign.

Negative Factors of 685: -1, -5, -137, -685

### Prime Factorization of 685

The prime factorization of 685Â is the way of expressing its prime factors in the product form.

Prime Factorization: 5 x 137

In this article, we will learn about the factors of 685 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 685?

The factors of 685 are 1, 5, 137, and 685. These numbers are the factors as they do not leave any remainder when divided by 685.

The factors of 685 are classified as prime numbers and composite numbers. The prime factors of the number 685 can be determined using the prime factorization technique.

## How To Find the Factors of 685?

You can find the factors of 685Â 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 685, create a list containing the numbers that are exactly divisible by 685 with zero remainders. One important thing to note is that 1 and 685 are the 685’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 685 are determined as follows:

$\dfrac{685}{1} = 685$

$\dfrac{685}{5} = 137$

$\dfrac{685}{137} = 5$

$\dfrac{685}{685} = 1$

Therefore, 1, 5, 137, and 685Â are the factors of 685.

### Total Number of Factors of 685

For 685, there are 4Â positive factors and 4Â negative ones. So in total, there are 8 factors of 685.Â

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 685 is given as:

Factorization of 685 is 1 x 5 x 137.

The exponent of 1, 5, and 127 is 1.

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

Therefore, the total number of factors of 685 is 8. 4 is 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 685 by Prime Factorization

The number 685Â is a composite/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 685 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 685, 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 685Â can be expressed as:

685 = 5 x 137

## Factors of 685Â 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 685, the factor pairs can be found as:

1 x 685 = 685

5Â  x 137= 685

The possible factor pairs of 685 are given asÂ (1, 685) and (5, 137 ).

All these numbers in pairs, when multiplied, give 685 as the product.

The negative factor pairs of 685 are given as:

-1 x -685 = 685

-5Â  x -137= 685

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, -5, -137,Â  and -685 are called negative factors of 685.

The list of all the factors of 685, including positive as well as negative numbers, is given below.

Factor list of 685: 1,-1, 5,-5, 137, -137,Â  685, and -685

## Factors of 685 Solved Examples

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

### Example 1

How many factors of 685 are there?

### Solution

The total number of Factors of 685 is 8.

Factors of 685 are 1, 5, 137, and 685.

### Example 2

Find the factors of 685 using prime factorization.

### Solution

The prime factorization of 685 is given as:

685 $\div$ 5 = 137

137 $\div$ 137 = 1

So the prime factorization of 685 can be written as:

5 x 137 = 685