 # Factors of 220: Prime Factorization, Methods, and Examples

The factors of 220 are the numbers that evenly divide 220 into equal parts without any residue. The number 220 is an even composite number with 12 factors in total. The factors of the given number can be positive as well as negative provided that the given number is achieved upon multiplication of two-factor integers.

### Factors of 220

Here are the factors of number 220.

Factors of 220: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220

### Negative Factors of 220

The negative factors of 220 are similar to its positive factors, just with a negative sign.

Negative Factors of 220: -1, -2, -4, -5, -10, -11, -20, -22, -44, -55, -110, -220

### Prime Factorization of 220

The prime factorization of 220 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 5 x 11

In this article, we will learn about the factors of 220 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 220?

The factors of 220 are a1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, and 220. All of these numbers are the factors as they do not leave any remainder when divided by 220.

The factors of 220 are classified as prime numbers and composite numbers. The prime factors of the number 220 can be determined using the technique of prime factorization.

## How To Find the Factors of 220?

You can find the factors of 220 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 220, create a list containing the numbers that are exactly divisible by 220 with zero remainders. One important thing to note is that 1 and 220 are the 220’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 220 are determined as follows:

$\dfrac{220}{1} = 220$

$\dfrac{220}{2} = 110$

$\dfrac{220}{4} = 55$

$\dfrac{220}{5} = 44$

$\dfrac{220}{10} = 22$

$\dfrac{220}{11} = 20$

$\dfrac{220}{220} = 1$

Therefore, 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, and 220 are the factors of 220.

### Total Number of Factors of 220

For 220 there are 12 positive factors and 12 negative ones. So in total, there are 24 factors of 220.

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

1. Find the 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 220 is given as:

Factorization of 220 is 1 x $2^2$ x 5 x 11.

The exponent of 1, 5, and 11 is 1. The exponent of 2 is 2.

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

Therefore, the total number of factors of 220 is 24. 12 are positive and 12 factors are negative.

### Important Notes

Here are some important 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 220 by Prime Factorization  The number 220 is a composite. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 220 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 220, start dividing by its smallest 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 220 can be expressed as:

220 = 2 x 2 x 5 x 11

## Factors of 220 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 of the given numbers.

For 220, the factor pairs can be found as:

1 x 220 = 220

2 x 110 = 220

4 x 55 = 220

5 x 44 = 220

10 x 22 = 220

11 x 20 = 220

The possible factor pairs of 220 are given as (1, 220), (2, 110), (4, 55), (5, 44), (10, 22), and (11, 20 ).

All these numbers in pairs, when multiplied, give 220 as the product.

The negative factor pairs of X are given as:

-1 x -220 = 220

-2 x -110 = 220

-4 x -55 = 220

-5 x -44 = 220

-10 x -22 = 220

-11 x -20 = 220

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, -11, -20, -22, -44, -55, -110, and -220 are called negative factors of 220.

The list of all the factors of 220 including positive as well as negative numbers is given below.

Factor list of 220: 1, -1, 2, -2, 4, -4, 5, -5, 10, -10, 11, -11, 20, -20, 22, -22, 44, -44, 55, -55, 110, -110, 220, and -220

## Factors of 220 Solved Examples

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

### Example 1

How many factors of 220 are there?

### Solution

The total number of Factors of 220 is 12.

Factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, and 220.

### Example 2

Find the factors of 220 using prime factorization.

### Solution

The prime factorization of 220 is given as:

220 $\div$ 2 = 110

110 $\div$ 2 = 55

55 $\div$ 5 = 11

11 $\div$ 11 = 1

So the prime factorization of 220 can be written as:

2 x 2 x 5 x 11 = 220