The **factors of 238** are the numbers that give 238 as the product when these two numbers are multiplied together. These numbers also produce zero as the remainder when they act as the divisor.

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 238

Here are the factors of number** 238.**

**Factors of 238**: 1, 2, 7, 14, 17, 34, 119, 238

### Negative Factors of 238

The **negative factors of 238**are similar to its positive factors, just with a negative sign.

**Negative Factors of 238**: -1, -2, -7, -14, -17, -34, -119, and -238

### Prime Factorization of 238

The **prime factorization of 238**is the way of expressing its prime factors in the product form.

**Prime Factorization**: 2 x 7 x 17

In this article, we will learn about the **factors of 238 **and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 238?

**The factors of 238 are 1, 2, 7, 14, 17, 34, 119, and 238. All of these numbers are the factors as they do not leave any remainder when divided by 238.**

The **factors of 238** are classified as prime numbers and composite numbers. The prime factors of the number 238 can be determined using the technique of prime factorization.

## How To Find the Factors of 238?

You can find the **factors of 238**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 238, create a list containing the numbers that are exactly divisible by 238 with zero remainders. One important thing to note is that 1 and 238 are the 238’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 238 are determined as follows:

\[\dfrac{238}{1} = 238\]

\[\dfrac{238}{2} = 119\]

\[\dfrac{238}{7} = 34\]

\[\dfrac{238}{14} = 17\]

\[\dfrac{238}{17} =14\]

\[\dfrac{238}{34} = 7\]

\[\dfrac{238}{119} = 2\]

\[\dfrac{238}{238} =1\]

Therefore, 1, 2, 7, 14, 17, 34, 119, and 238 are the factors of 238.

### Total Number of Factors of 238

For 238 there are 8**positive factors** and 8**negative** ones. So in total, there are 16 factors of 238.

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

- Find the 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 238 is given as:

Factorization of 238 is** 1 x 2 x 7 x 17**

The exponent of all factors is 1.

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

Therefore, the **total number of factors** of 238 is 16. 8 are positive and 8 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 238 by Prime Factorization

The **number 238** is a composite number. 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 238 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 238, 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 238**can be expressed as:

**238 = 2 x 7 x 17**

## Factors of 238 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 238, the factor pairs can be found as:

**1 x 238 = 238**

**2 x 119 = 238**

**7 x 34 = 238**

**14 x 17 = 238**

The possible** factor pairs of 238 **are given as**(1, 238), (2, 119), (7, 34), **and **(14****, 17)**.

All these numbers in pairs, when multiplied, give 238 as the product.

The **negative factor pairs** of 238 are given as:

**-1 x -238 = 238**

**-2 x -119 = 238**

**-7 x -34 = 238**

**-14 x -17 = 238**

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, -7, -14, -17, -34, -119, and -238 are called negative factors of 238.

The list of all the factors of 238 including positive as well as negative numbers is given below.

**Factor list of 238: 1, -1, 2, -2, 7, -7, 14, -14, 17, -17, 34, -34, 119, -119, 238, and -238**

## Factors of 238 Solved Examples

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

### Example 1

How many factors of 238 are there?

### Solution

The total number of Factors of 238 is 8.

Factors of 238 are 1, 2, 7, 14, 17, 34, 119, and 238.

### Example 2

Find the factors of 238 using prime factorization.

### Solution

The prime factorization of 238 is given as:

**238 $\div$ 2 = 119**

**119 $\div$ 7 = 17**

**17 $\div$ 17 =1**

So the prime factorization of 238 can be written as:

**2 x 7 x 17 = 238**