# Factors of 238

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

#### How to find factors of a number

 1.   Find factors of 238 using Division Method 2.   Find factors of 238 using Prime Factorization 3.   Find factors of 238 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 238

• Divide 238 by 1: 238 ÷ 1 : Remainder = 0
• Divide 238 by 2: 238 ÷ 2 : Remainder = 0
• Divide 238 by 7: 238 ÷ 7 : Remainder = 0
• Divide 238 by 14: 238 ÷ 14 : Remainder = 0
• Divide 238 by 17: 238 ÷ 17 : Remainder = 0
• Divide 238 by 34: 238 ÷ 34 : Remainder = 0
• Divide 238 by 119: 238 ÷ 119 : Remainder = 0
• Divide 238 by 238: 238 ÷ 238 : Remainder = 0

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

#### 2. Steps to find factors of 238 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 238 using the division method, follow these steps:

• Step 1. Start dividing 238 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 238, which is 2. Divide 238 by 2 to obtain the quotient (119).
238 ÷ 2 = 119
• Step 3. Repeat step 1 with the obtained quotient (119).
119 ÷ 7 = 17
17 ÷ 17 = 1

So, the prime factorization of 238 is, 238 = 2 x 7 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 238 as shown below:

So, the prime factorization of 238 is, 238 = 2 x 7 x 17.

#### 3. Find factors of 238 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 238 would be the two numbers which, when multiplied, give 238 as the result.

The following table represents the calculation of factors of 238 in pairs:

Factor Pair Pair Factorization
1 and 238 1 x 238 = 238
2 and 119 2 x 119 = 238
7 and 34 7 x 34 = 238
14 and 17 14 x 17 = 238

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 238. They are called negative pair factors.

Hence, the negative pairs of 238 would be ( -1 , -238 ) , ( -2 , -119 ) , ( -7 , -34 ) and ( -14 , -17 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 238 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 7, 14, 17, 34, 119, 238 are exact divisors of 238.
• 1 is a factor of every number. Eg. 1 is a factor of 238.
• Every number is a factor of zero (0), since 238 x 0 = 0.

• Is 238 a perfect square?

No 238 is not a perfect square.

• What are factors of 238?

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

• Which is greatest factor of 238?

The greatest factor of 238 is 119.

• What is the sum of all factors of 238?

The sum of all factors of 238 is 432.

• What are multiples of 238?

First five multiples of 238 are 476, 714, 952, 1190.

• What is the greatest prime factors of 238?

The greatest prime factor of 238 is 17.

• What are six multiples of 238?

First five multiples of 238 are 476, 714, 952, 1190, 1428, 1666.

• What is prime factorization of 238?

Prime factorization of 238 is 2 x 7 x 17.

• Is 238 a whole number?

Yes 238 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 238? Help her in writing all the factors.

Positive factors are 1, 2, 7, 14, 17, 34, 119, 238.
Negative factors are -1, -2, -7, -14, -17, -34, -119, -238.

Can you help Sammy find out the product of the odd factors of 238?

Factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238.
Odd factors of 238 are 1, 7, 17, 119.
Hence product of odd factors of 238 is; 1 x 7 x 17 x 119 = 14161.

Joey wants to write all the prime factors of 238 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 238 are 2, 7, 17.
So in exponential form it can be written as 2 x 7 x 17.

How many factors are there for 238?

Factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 238. Can you predict the answer?

7 factor(s) of 238 are 1, 2, 7, 14, 17, 34, 119.

Sammy is puzzled while calculating the prime factors of 238. Can you help him find them?

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

What is prime factorization of 238?

Prime factorization of 238 is 2 x 7 x 17 = 2 x 7 x 17.