# Factors of 38

Factors of 38 are 1, 2, 19, and 38

#### How to find factors of a number

 1.   Find factors of 38 using Division Method 2.   Find factors of 38 using Prime Factorization 3.   Find factors of 38 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 38

• Divide 38 by 1: 38 ÷ 1 : Remainder = 0
• Divide 38 by 2: 38 ÷ 2 : Remainder = 0
• Divide 38 by 19: 38 ÷ 19 : Remainder = 0
• Divide 38 by 38: 38 ÷ 38 : Remainder = 0

Hence, Factors of 38 are 1, 2, 19, and 38

#### 2. Steps to find factors of 38 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 38 using the division method, follow these steps:

• Step 1. Start dividing 38 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 38, which is 2. Divide 38 by 2 to obtain the quotient (19).
38 ÷ 2 = 19
• Step 3. Repeat step 1 with the obtained quotient (19).
19 ÷ 19 = 1

So, the prime factorization of 38 is, 38 = 2 x 19.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 38 as shown below:

So, the prime factorization of 38 is, 38 = 2 x 19.

#### 3. Find factors of 38 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 38 would be the two numbers which, when multiplied, give 38 as the result.

The following table represents the calculation of factors of 38 in pairs:

Factor Pair Pair Factorization
1 and 38 1 x 38 = 38
2 and 19 2 x 19 = 38

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 38. They are called negative pair factors.

Hence, the negative pairs of 38 would be ( -1 , -38 ) , ( -2 , -19 ) .

#### 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. 38 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, 19, 38 are exact divisors of 38.
• 1 is a factor of every number. Eg. 1 is a factor of 38.
• Every number is a factor of zero (0), since 38 x 0 = 0.

• What two numbers make 38?

Two numbers that make 38 are 2 and 19.

• What is prime factorization of 38?

Prime factorization of 38 is 2 x 19.

• Write some multiples of 38?

First five multiples of 38 are 76, 114, 152, 190.

• Which is the smallest prime factor of 38?

The smallest prime factor of 38 is 2.

• Is 38 a perfect square?

No 38 is not a perfect square.

• What is the sum of all factors of 38?

The sum of all factors of 38 is 60.

• What are factors of 38?

Factors of 38 are 1, 2, 19, 38.

• How do you find factors of a negative number? ( eg. -38 )?

Factors of -38 are -1, -2, -19, -38.

• Is 38 a whole number?

Yes 38 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 38. Help him in finding the mean of 38.

Factors of 38 are 1, 2, 19, 38.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 38 is 1 + 2 + 19 + 38 = 60.
Hence, the mean of factors of 38 is 60 ÷ 4 = 15.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 38? Help her in writing all the factors.

Positive factors are 1, 2, 19, 38.
Negative factors are -1, -2, -19, -38.

Joey wants to write all the prime factors of 38 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 38 are 2, 19.
So in exponential form it can be written as 2 x 19.

Kevin has been asked to write 3 factor(s) of 38. Can you predict the answer?

3 factor(s) of 38 are 1, 2, 19.

Sammy is puzzled while calculating the prime factors of 38. Can you help him find them?

Factors of 38 are 1, 2, 19, 38.
Prime factors of 38 are 2, 19

What is prime factorization of 38?

Prime factorization of 38 is 2 x 19 = 2 x 19.

Can you help Rubel to find out the product of the even factors of 38?

Factors of 38 are 1, 2, 19, 38.
Even factors of 38 are 2, 38.
Hence, product of even factors of 38 is; 2 x 38 = 76.