# Factors Of 42 | With Easy Division and Prime Factorization

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## Factors Of 42

A factor of 42 is a pair of numbers that, when multiplied together, give the original number.  Similarly, composite numbers such as 48, 60, 70, 420, 36, 45, 30, etc. have prime factorization that can be determined.

It is rather simple and easy to discover the factors of a number of 42. Basically, you multiply two numbers together to get another number.

With the prime factorization method, we will discover the factors of 42, as well as the prime factors and pair factors.

## What are the Factors of 42?

Numbers dividing 42 exactly without remainder are called 42’s factors. Due to its composite nature, the number 42 has many factors besides one and itself.

It is possible to divide 42 by positive or negative factors, but not in decimal or fraction form. As a result, 42 has the factors 1, 2, 3, 6, 7, 14, 21, and 42.

Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42.

Prime Factorization of 42: 2 × 3 × 7

## What are the Factors Of -42?

Factors of -42: -1, -2, -3, -6, -7, -14, -21 and -42.

The number -42 can be calculated by multiplying two numbers together:

-1 x  42 =  -42    &   1 x -42 =   -42

-2 x  21 =   -42     &  2 x  -21 =   -42

-14 x  3 =  -42    &  14 x  -3 =   -42

-7 x  6 =  -42    &  7 x  -6 =   -42

## Pair Factors of 42

By multiplying two numbers together to get 42, we can find the factors that make up 42. To do so, follow these steps:

1 × 42 = 42

2 × 21 = 42

3 × 14 = 42

6 × 7 = 42

As a consequence, the pair factors of 42 are (1, 42), (2, 21), (3, 14), and (6, 7).

## Prime Factorization of 42

In mathematics, the number 42 is a composite number. Here are the prime factors of 42.

It is essential to divide 42 by the smallest prime factor, i.e. 2.

42 ÷ 2 = 21

Try to divide 21 by 2 again.

21 ÷ 2 = 10.5

However, a factor can never be a fraction. Let’s move on to the next prime number.

When we divide 21 by 3, we get:

21 ÷ 3 = 7

Divide 7 by 3 again to get a fraction. Therefore, we should take 5 into account.

21 ÷ 5 = 4.2, again a fraction number.

Next, we have 7.

7 ÷ 7 = 1

We have received 1 at the end, so we cannot proceed with the division method, because 1 is the only multiple of 1.

Therefore, 42 has a prime factorization of 2 × 3 × 7, where 2, 3, and 7 are prime numbers.

## Examples

### Example 1:

Find the common factor between 42 and 24.

Solution:

42 has the factors 1, 2, 3, 6, 7, 14, 21, and 4

Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24.

The common factor between 42 and 24 is 1, 2, 3, and 6..

### Example 2:

Calculate the common factors of 3 and 43.

Solution:

Factors of 3 are 1 and 3.

All the Factors of 43 = 1 and 43.

Therefore, 3 and 43 have a common factor of 1.

### Example 3:

Identify the common factors between 42 and 45.

Solution:

42 has the factors 1, 2, 3, 6, 7, 14, 21, and 42.

All the Factors of 45 = 1, 3, 5, 9, 15, and 45.

As a result, 42 and 45 have 1 and 3 in common.

## FAQs

### How many factors are there in 42?

Factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

### What is the prime factorization of 42?

42 has a prime factorization of 2 × 3 × 7.

### Write down the positive pair factors for 42.

For 42, the positive pair factors are (1, 42), (2, 21), (3, 14), and (6, 7).

### The negative pair factors of 42 are?

There are four negative pair factors of 42: (-1, -42), (-2, -21), (-3, -14), and (-6, -7).

### 21 is a factor of 42, right?

In fact, 21 is a factor of 42. Since 21 divides 42 exactly, 21 is a factor of 42.