# Factors of 38

Understanding Prime and Composite Numbers When studying mathematics, one of the fundamental concepts that students learn is that of prime and composite numbers. In this article, we will delve into the factors of 38, a composite number, and explore the various ways in which it can be broken down into its component parts.

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Prime Numbers

A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. Some examples of prime numbers include 2, 3, 5, 7, and 11. Prime numbers are important in mathematics as they are used in many mathematical formulas and algorithms, and are also used in the study of number theory.

Composite Numbers

A composite number is a whole number greater than 1 that can be divided evenly by a number other than 1 or itself. In other words, a composite number is not a prime number. Some examples of composite numbers include 4, 6, 8, 9, and 10.

## What are the factors of 38?

The method of calculating the factors of 38 is as follows. First, each number can be divided by one and by itself.

Consequently, 1 and 38 are the factors of 38.
By dividing a number by 1, 2, 3, 4… we can discover all its factors.

(i) 38 ÷ 1 = 38

This division gives the remainder 0 and so is divisible by 38. So please put them 1 and 38 in your factor list.

1, …….. 38

(ii) 38 ÷ 2 = 19

This division gives the remainder 0 and so is divisible by 19. So please put them 2 and 19 in your factor list.

1, 2 …….. 19, 38

(iii) 38 ÷ 3 = 12.66

This division gives the remainder 12.66, not being thoroughly divided. So we will not write 3 and 12.66 on the list.

(iv) 38 ÷ 4 = 9.5

This division gives the remainder 9.5, not being thoroughly divided. So we will not write 4 and 9.5 on the list.

(iv) 38 ÷ 5 = 7.2

This division gives the remainder 7.6, not being thoroughly divided. So we will not write 5 and 7.6 on the list.

(v) Since we don’t have any more numbers to calculate, we are putting the numbers so far.

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

## Factor pairs of 38

1 x 38 = 38
2 x 19 = 38

So, (1, 38) and (2, 19) are factor pairs of 38

## Factor pairs of -38

-1 x -38 = 38
-2 x -19 = 38

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

## Prime Factorization of 38

38 ÷ 2 = 19
19 ÷ 19 = 1

Therefore, 2 × 19 are Prime factorization of 38.

## Factor tree of 38

``````         38
/  \
2    19``````