Factors

# Factors of 38 | Prime Factorization of 38 | Factor Tree of 38

Written by Prerit Jain

Updated on: 18 Aug 2023

### Factors of 38 | Prime Factorization of 38 | Factor Tree of 38

Factors of 38: Factors are numbers or mathematical expressions that can divide another number evenly. That means there is no remainder left.

38 has 4 factors in total. They are 1, 2, 19, and 38.

A number can have factors that are positive or negative. They are also written in the pairs. In this article, we will find factors of 38, its prime factorization, and factor trees with solved examples. To learn more, continue reading.

## What Are the Factors of 38?

The factors of 38 are the numbers that divide the number 38 evenly, without a remainder. The number 38 has both positive and negative factors.

## What Are the Factors of 38 in Pairs?

A pair factor of 38 is a combination of two numbers, which when multiplied together gives the product of the original number (38). These pair factors are also written in positive and negative pairs as shown in the table below:

### Positive Pair Factors of 38

The positive pair factors of 38 are (1, 38) and (2, 19).

### Negative Pair Factors of 38

The negative pair factors of 38 are (-1, -38) and (-2, -19).

## How To Find Factors of 38 Using the Division Method?

To find the factors of 38, we are using the division method. In this method, we are required to multiply a sequence of natural integers by 38. The numbers that divide the 38 completely without leaving any remainder are its factors. The following are the detailed steps for finding factors of 38 using the division method:

38 ÷ 1 = 38

38 ÷ 2 = 19

38 ÷ 19 = 2

38 ÷ 38 = 1

We can observe that 1, 2, 19, and 38 are the numbers that do not leave any remainder when divided by 38. So, the factors of 38 are 1, 2, 19, and 38.

## What Is the Prime Factorization of 38?

Before performing prime factorization, we must first check if the given number is a prime number. If it is, it has only two factors: 1 and 38. If a number is a composite number, then it has more than two factors.

38 is the composite number and had more than 2 factors. So, we can use the prime factorization method to find the factors of 38.

The steps to find prime factors of 38 using the prime factorization method are given below:

Step 1: Divide the number 38 with the smallest prime number that can divide it. The smallest prime number that can divide 38 is 2. So, 38 ÷ 2 = 19

Step 2: We should now divide the quotient with another prime number. But 19 happens to be a prime number as well. So, it can only be divided by 19 and 1. Dividing 19 with 19 gives us 1. So, 19 ÷ 19 = 1

Step 3: The quotient is 1. Since 1 cannot be divided further, the prime factors of 38 are 2 X 19. We can also write it down as 2 and 19, as both of them are prime numbers.

Pictorial representation of the prime factorization of 38:

## What is the Factor Tree of 38?

We can also employ the factor tree method to find the prime factors of 38. This method will require us to place the number 38 on top of the factor tree. As part of the branches, we will write down any pair factors of 38. We will again split the pair of factors into factors. This process will go on until the branches become prime numbers.

Step 1: Let’s place the number 38 at the top of the factor tree and write down 38 in pairs. For example- 2 and 19.

Step 2: Both 2 and 19 are prime numbers. So, we can no longer separate them. This brings us to the end of the factor tree.

Hence, circling all the branches, 2 X 19= 38, which are 38 prime factors.
There are many ways to write the factor tree of 38. Below is an image representation of the factor tree of 38, choosing 2 and 19 as pair factors of 38.

## Solved Examples on Factors of 38

Here are some solved examples of factors of 38:

What is the sum of all the factors of 38?
1, 2, 19, and 38 are the 38 factors.
1 + 2 + 19 + 38 = 60
Hence, 60 is the sum of all 38 factors.

What are the factors and prime factors of 38?
The factors of 38 are 1, 2, 19, and 38.
The prime factors of 38 are 2 X 19.

What’s the highest common factor between 38 and 57?
Factors of 38 are 1, 2, 19, and 38.
Factors of 57 are 1, 3, 19, and 57.
Hence, from the above, the common factors of 38 and 57 are 1 and 19.
The highest common factor between 38 and 57 is 19.

What’s the highest common factor between 38 and 95?
Factors of 38 are 1, 2, 19, and 38.
Factors of 95 are 1, 5, 19, and 95.
Hence, from the above, the common factors of 38 and 95 are 1 and 19.
The highest common factor between 38 and 95 is 19.

Is 2 a factor of 38?
Yes, 2 is a factor of 38.
As 38 ÷ 2 = 19.

What are the factors of -38?
The factors of -38 are -1, -2, -19 and -38.

What are the common factors of 38 and 46?
To find the common factors of 38 and 46, we need to find the factors of both numbers.
Factors of 38: 1, 2, 19 and 38
Factors of 46: 1, 2, 23 and 46
Hence the common factors of 38 and 46 are 1 and 2.

What are all the factors of 38?
The factors of 38 are 1, 2, 19, and 38.

What are the factors of 38 that are composite?
Any number which has more than 2 factors is known as a composite number. The number which has more than 2 factors in the factors of 38 is 38.

What factors of 38 are multiples of 2?
The factors of 38 that are multiples of 2 are 2 and 38.
2x 1 = 2
2 x 19 = 38.

How many factors of 38 are odd?
A total of 2 odd numbers are there in factors of 38 and they are 1 and 19.

What are the factors of 38 and 19?
The factors of 38 are 1, 2, 19, and 38.
The factors of 19 are 1 and 19.

What are the common factors of 38 and 58?
To list out the common factors of 38 and 58, we need to find the factors of both numbers.
Factors of 38: 1, 2, 19 and 38
Factors of 58: 1, 2, 29 and 58
From the above, the common factors of 38 and 58 are 1 and 2.

How many different factors are there for the number 38?
A total of 4 factors are there for the number 38 and they are 1, 2, 19, and 38.

How many pair factors are there in 38?
A total of 2 pairs are there in factors of 38 and they are (1, 38) and (2, 19).

What is the largest factor of 38?
The largest factor of 38 is 38.
The second largest factor of 38 is 19.

## FAQs on Factors of 38

List all the factors of 38
1, 2, 19, and 38 are the 38 factors.

What are the composite factors of 38?
Only 38 is a composite factor of 38. Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 38 in pairs?
(1, 38) and (2, 19) are the factors of 38 in pairs.

What are the positive factors for 38?
1, 2, 19, and 38 are the positive factors for 38.

Does 38 have negative factors? If so, what are they?
Yes, 38, like all numbers has negative factors. They are -1, -2, -19, and -38.

We have now read all about the factors of 38. We hope this blog has been simple to understand, as well as, useful.

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Prerit Jain

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