# Factors of 442: Prime Factorization, Methods, and Examples

The factors of 442Â are the listing of the numbers that divide 442 evenly. There are 8 factors of 442. It is called a composite number because it has more than two factors.Â

Let us explore more about the factors of 442.

### Factors of 442

Here are the factors of numberÂ 442.

Factors of 442: 1, 2, 13, 17, 26, 34, 221, and 442Â

### Negative Factors of 442

The negative factors of 442Â are similar to their positive aspects, just with a negative sign.

Negative Factors of 442: –1, -2, -13, -17, -26, -34, -221, and -442Â

### Prime Factorization of 442

The prime factorization of 442Â is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 13 x 17

In this article, we will learn about the factors of 442Â and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 442?

The factors of 442 areÂ 1, 2, 13, 17, 26, 34, 221, and 442. These numbers are the factors as they do not leave any remainder when divided by 442.

The factors of 442Â are classified as prime numbers and composite numbers. The prime factors of the number 442 can be determined using the prime factorization technique.

## How To Find the Factors of 442?

You can find the factors of 442Â 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 442, create a list containing the numbers that are exactly divisible by 442 with zero remainders. One important thing to note is that 1 and 442 are the 442’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 442 are determined as follows:

$\dfrac{442}{1} = 442$

$\dfrac{442}{2} = 221$

$\dfrac{442}{13} = 34$

$\dfrac{442}{17} = 26$

Therefore,Â 1, 2, 13, 17, 26, 34, 221, and 442Â are the factors of 442.

### Total Number of Factors of 442

For 442, there are eightÂ positive factors and eightÂ negative ones. So in total, there are sixteen factors of 442.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 442 is given as:

Factorization of 442 isÂ 1 x 2 x 13 x 17.

The exponent of 1, 2, 13, and 17 is 1.

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

Therefore, the total number of factors of 442 is 16. Eight are positive, and eight 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 442 by Prime Factorization

The number 442Â is a composite. 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 442 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 442, 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 442Â can be expressed as:

442 = 2 x 13 x 17

## Factors of 442 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 442, the factor pairs can be found as:

1 x 442 = 442

2 x 221 = 442

13 x 34 = 442Â

17 x 26 = 442

The possible factor pairs of 442Â are given asÂ (1, 442), (2, 221), (13, 34),Â and (17, 26).

All these numbers in pairs, when multiplied, give 442 as the product.

The negative factor pairs of 442 are given as:

-1 x -442 = 442

-2 x -221 = 442

-13 x -34 = 442Â

-17 x -26 = 442

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, -13, -17, -26, -34, -221, and -442Â are called negative factors of 442.

The list of all the factors of 442, including positive as well as negative numbers, is given below.

Factor list of 442:Â 1, -1, 2, -2, 13, -13, 17, -17, 26, -26, 34, -34, 221, -221, 442 and -442

## Factors of 442 Solved Examples

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

### Example 1

How many factors of 442 are there?

### Solution

The total number of Factors of 442 is eight.

Factors of 442 areÂ 1, 2, 13, 17, 26, 34, 221, and 442.

### Example 2

Find the factors of 442 using prime factorization.

### Solution

The prime factorization of 442 is given as:

442 $\div$ 2 = 221Â

221 $\div$ 11 = 17Â

17 $\div$ 17 = 1Â

So the prime factorization of 442 can be written as:

2 x 11 x 17 = 442