 # Factors of 820: Prime Factorization, Methods, and Examples

820 has a total of 12 factors. The list of factors of 820 has both prime and composite numbers. The number of prime factors is 3 where 2 is its smallest prime factor while all other factors are composite numbers. The factors of 820 are all smaller than 820 as it is the multiple of its factors.

### Factors of 820

Here are the factors of number 820.

Factors of 820: 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, and 820

### Negative Factors of 820

The negative factors of 820 are similar to its positive aspects, just with a negative sign.

Negative Factors of 820: -1, -2, -4, -5, -10, -20, -41, -82, -164, -205, -410, and -820

### Prime Factorization of 820

The prime factorization of 820 is the way of expressing its prime factors in the product form.

Prime Factorization: 2$^2$ x 5 x 41

In this article, we will learn about the factors of 820 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 820

The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, and 820. These numbers are the factors as they do not leave any remainder when divided by 820.

The factors of 820 are classified as prime numbers and composite numbers. The prime factors of the number 820 can be determined using the prime factorization technique.

## How To Find the Factors of 820?

You can find the factors of 820 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 820, create a list containing the numbers that are exactly divisible by 820 with zero remainders. One important thing to note is that 1 and 820 are the 820’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 820 are determined as follows:

$\dfrac{820}{1} = 820$

$\dfrac{820}{2} = 410$

$\dfrac{820}{4} = 205$

$\dfrac{820}{5} = 164$

$\dfrac{820}{10} = 82$

$\dfrac{820}{20} = 41$

$\dfrac{820}{41} = 20$

$\dfrac{820}{82} = 10$

$\dfrac{820}{164} = 5$

$\dfrac{820}{205} = 4$

$\dfrac{820}{410} = 2$

$\dfrac{820}{820} = 1$

Therefore, 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, and 820 are the factors of  820.

### Total Number of Factors of 820

For 820, there are 12 positive factors and 12 negative ones. So in total, there are 24 factors of 820.

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 820 is given as:

Factorization of 820 is 1 x 2$2$ x 5 x 41.

The exponent of 1, 5, and 41 is 1 and the exponent of 2 is 2.

Adding 1 to each and multiplying them together results in 24.

Therefore, the total number of factors of 820 is 24. 12 are positive, and 12 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 820 by Prime Factorization

The number 820 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 820 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 820, 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 820 can be expressed as:

820 = 2$^2$ x 5 x 41

## Factors of 820 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 820, the factor pairs can be found as:

1 x 820 = 820

2 x 410 = 820

4 x 205 = 820

5 x 164 = 820

10 x 82 = 820

20 x 41 = 820

The possible factor pairs of 820 are given as (1, 820), (2, 410), (4, 205), (5, 164), (10, 82) and (20, 41).

All these numbers in pairs, when multiplied, give 820 as the product.

The negative factor pairs of 820 are given as:

-1 x -820 = 820

-2 x -410 = 820

-4 x -205 = 820

-5 x -164 = 820

-10 x -82 = 820

-20 x -41 = 820

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, -10, -20, -41, -82, -164, -205, -410, and 820 are called negative factors of 820.

The list of all the factors of 820, including positive as well as negative numbers, is given below.

Factor list of 820: 1, -1, 2, -2, 4, -4, 5, -5, 10, -10, 20, -20, 41, -41, 82, -82, 164, -164, 205, -205, 410, -410, 820, and -820.

## Factors of 820 Solved Examples

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

### Example 1

How many factors of 820 are there?

### Solution

The total number of Factors of 820 is 12.

Factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, and 820.

### Example 2

Find the factors of 820 using prime factorization.

### Solution

The prime factorization of 820 is given as:

820 $\div$ 2 = 410

410 $\div$ 2 = 205

205 $\div$ 5 = 41

14 $\div$ 41 = 1

So the prime factorization of 820 can be written as:

2$^2$ x 5 x 41 = 820