Factors of 38 | Division & Prime Factorization | Easy Way

Factors Of 38

Real numbers are the factors of 38 that divide the original number equally. There is no remainder left after 38 is divided by its factor. As we know, 38 will have more than two factors due to their composite nature.

By multiplying consecutive natural numbers by 38, multiples are generated. Factors and multiples have different meanings. However, 38 is both a factor and a multiple of itself, since,

38 x 1 = 38  (Multiple)

38/38 = 1     (Factor)

Let’s see how to find the factors of 38, the pair factors, and the prime factors.

How to Find Factors of 38?

A factor of 38 is an integer that can completely divide the original number. To find the factors, we must determine which of the following numbers is completely divisible by 38. Let’s begin by dividing 38 by 1, the smallest natural number.

38 ÷ 1 = 38

38 ÷ 2 = 19

38 ÷ 19 = 2

38 ÷ 38 = 1

Accordingly, 1, 2, 19, and 38 are the factors of 38.

Factors of -38

In the case of -38, the factors will be the additive inverse of natural numbers, i.e., negative numbers. Dividing -38 by any negative number will produce a positive number.

• (-38) ÷ (-1)    = 38
• (-38) ÷ (-2)    = 19
• (-38) ÷ (-19)  = 2
• (-38) ÷ (-38)  = 1

Consequently,  -1, -2, -19 and -38 are the factors of -38.

Pair Factors of 38

After getting multiplied together, the factors of 38 result in the original number, such that;

1 × 38 = 38

2 × 19 = 38

As a result, (1, 38) and (2, 19) are the pair factors.

As a result, the original number will also be obtained if we multiply the negative pair factors. Since then,

-1 × -38 = 38

-2 × -19 = 38

As a result, the negative pair factors are (-1, -38) and (-2, -19).

Notable: 

Because they produce the original number when multiplied in pairs, they are called pair factors. We won’t get the actual result if you modify the pair.

Prime Factorization of 38

Primarily, a number is factorized by its prime factors. There are two prime factors of these prime numbers, one and the number itself. For example, 2, 3, 5, 7, 11, and so on.

First, we have to find out if 38 is completely divisible by the prime number before finding its prime factors. So, we will divide 38 by the smallest prime factor, i.e., 2.

When we divide 38 by 2, we get;

38/2 = 19

In other words, 2 is one of the important prime factors

Since 19 is a prime number, it can only be divided by 19.

19/19 = 1

Another prime factor is 19

It is now impossible to divide further. As a consequence, 2 and 19 are prime factors of 38.

Prime factorization of 38 = 2 x 19

Solved Example

1. On Roy’s birthday, he distributes chocolates to his classmates. How many chocolates does each student get if there are 38 chocolates and 19 students?

Solution: 

Number of chocolates = 38

Student count = 19

This means that each student received two chocolates 

= 38/19 

= 2

Calculate the sum of all the factors of 38. Find the average as well.

Solution: 

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

Sum = 1+2+19+38 = 60

Hence, the required sum is 60.

Our next step is to divide the total by the number of factors to find the average.

Since,

Average = 60/4 = 15

2. What are the factors in 35 and 38 that are the same?

Solution:

The numbers 35 and 38 are composite. Therefore, they have the following factors:

Factors of 35 →  1, 5, 7, and 35

38 → 1, 2, 19 and 38

There are two common factors in 35 and 38, namely: 1.

Similarly, common factors in 38 and factors of 24, namely 1, and 2.

FAQs

Conclusion

we hope that with the above illustration you are now in a better position to understand the factors of 35.

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