Factors

# Factors of 42 | Prime Factorization of 42 | Factor Tree of 42

Written by Prerit Jain

Updated on: 18 Aug 2023

### Factors of 42 | Prime Factorization of 42 | Factor Tree of 42

Factors of 42: Factors of a number are those that can divide that number (42) evenly, and not leave any reminders behind. 42 has 8 factors

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

42, like all numbers, has factors that are both positive and negative. They can also be written in pairs. So, multiplying the numbers within a pair can give the product of the given number (42).

We will learn about how to find the factors of 42 in this article We will also learn its prime factorization, and factor trees with solved examples.

## What Are the Factors of 42?

The factors of 42 are the numbers that can divide the number 42 evenly without leaving any remainder. The factors of a number can be positive and negative. So, the number 42 has both positive and negative factors.

## What Are the Factors of 42 in Pairs?

The pair factors of a number are a combination of two numbers when multiplied will give the product of the given number. In this case, we will be looking at the pair factors of 42.

### Positive Pair Factors of 42

The positive pair factors of 42 are (1, 42); (2, 21); (3, 14), and (6, 7).

### Negative Pair Factors of 42

The negative pair factors of 42 are (1, 42); (2, 21); (3, 14) and (6, 7).

## How To Find Factors of 42 Using the Division Method?

To find the factors of 42, we are going to use the division method. In this approach, we will multiply a sequential set of natural integers by 42. We will then find the numbers that divide 42 completely without leaving any remainder. The detailed steps to do the division method are given below:

42 ÷ 1 = 42

42 ÷ 2 = 21

42 ÷ 3 = 14

42 ÷ 6 = 7

42 ÷ 7 = 6

42 ÷ 14 = 3

42 ÷ 21 = 2

42 ÷ 42 =1

So, we can observe that 1, 2, 3, 6, 7, 14, 21, and 42 are the numbers that do not leave any remainder when divided by 42. Thus, the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

## What Is the Prime Factorization of 42?

Now let us use the prime factorization method to find the factors of 42. First, we need to check if the given number is a prime number. If so, it has only two factors: 1 and 42. If the number is a composite number, then it has more than two factors.
42 is the composite number so, it has more than two factors. We can use the prime factorization method to find its factors.

The steps to find prime factors of 42 using the prime factorization method are given below:

Step 1: Divide the number 42 with the smallest prime number that can divide it. That number is 2.
42 ÷ 2 = 21

Step 2: We got the quotient 21. Now, we will divide 21 by the smallest prime number, which is 3.
21 ÷ 3 = 7

Step 3: Now we got 7 as the quotient. Dividing 7 with 7 gives us 1.
7 ÷ 7 = 1

The quotient is 1. Since 1 cannot be divided further, the prime factors of 42 are 2 X 3 X 7. We can also write it down as 2, 3, and 7, as all three of them are prime numbers.

Image representation of the prime factorization of 42:

## What is the Factor Tree of 42?

We can also use the factor tree method to find the factors of 42. In this method, we will place the number 42 at the top of the factor tree. Next, we will write down any set of pair factors 42, as part of its branches. We will split the pair of factors further. We will continue this process until the branches become prime numbers.

Step 1: Let’s place the number 42 at the top of the factor tree. Then, write down 42 in pairs, that is, 7 and 6.

Step 2: 7 is a prime number and we can no longer separate it. We will now divide 6 into 2 and 3. As we can see, 2 and 3 are both prime numbers. The branches in the factor tree are all prime numbers.

Hence, circling all the branches, 2 X 3 X 7 = 42, which are 42 prime factors.
There are many ways in which we can write the factor tree of 42. Below is an image representation of the factor tree of 42, choosing 7 and 6 as pair factors of 42.

## Solved Examples on Factors of 42

Here are some solved examples of 42 factors:

What is the sum of all the factors of 42?
1, 2, 3, 6, 7, 14, 21, and 42 are the 42 factors.
1 + 2 + 3 + 6 + 7 + 14 + 21 + 42 = 96
Hence, 96 is the sum of all 42 factors.

What are the factors and prime factors of 42?
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
The prime factors of 42 are 2 X 3 X 7.

What’s the highest common factor between 42 and 162?
Factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
Factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81 and 162.
Hence, from the above, the common factors of 42 and 162 are 1, 2, 3, and 6.
The highest common factor between 42 and 162 is 6.

What’s the highest common factor between 36 and 42?
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
Hence, from the above, the common factors of 36 and 42 are 1, 2, 3, and 6.
The highest common factor between 36 and 42 is 6.

Is 14 a factor of 42?
Yes, 14 is a factor of 42.
42 ÷ 3 = 14.

What are the factors of -42?
The factors of -42 are -1, -2, -3, -6, -7, -14, -21 and -42.

What are the common factors of 42 and 90?
To find the common factors of 42 and 90, we need to find the factors of both numbers.
Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
Hence the common factors of 42 and 90 are 1, 2, 3, and 6.

What are all the factors of 42?
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

What are the factors of 42 that are composite?
Any number which has more than 2 factors is known as a composite number. The list of number which has more than 2 factors in factors of 42 is 6, 14, 21, and 42.
Hence the factors of 42 that are composite are 6, 14, 21, and 42.

What factors of 42 are multiples of 7?
The factors of 42 that are multiples of 7 are 7, 14, 21, and 42.
7 x 1 = 7
7 x 2 = 14
7 x 3 = 21
7 x 6 = 42.

How many 42 factors are odd?
A total of 4 odd numbers are there in factors of 42 and they are 1, 3, 7, and 21.

What are the factors of 42 and 98?
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
The factors of 98 are 1, 2, 7, 14, 49, and 98.

What are the common factors of 42 and 21?
To list out the common factors of 42 and 21, we need to find the factors of both numbers.
Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42
Factors of 21: 1, 3, 7 and 21
From the above, the common factors of 42 and 21 are 1, 3, and 7.

How many different factors are there for the number 42?
A total of 8 factors are there for the number 42 and they are 1, 2, 3, 6, 7, 14, 21, and 42.

What factors of 42 are multiples of 2?
The factors of 42 that are multiples of 2 are 2, 6, 14, and 42.

How many pair factors are there in 42?
A total of 4 pairs are there in factors of 42. They are (1, 42); (2, 21); (3, 14); (6, 7).

What is the largest factor of 42?
The largest factor of 42 is 42.
The second largest factor of 42 is 21.

## FAQs on Factors of 42

List all the factors of 42
1, 2, 3, 6, 7, 14, 21, and 42 are the 42 factors.

What are the composite factors of 42?
6, 14, 21, and 42 are the 42 composite factors.
Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 42 in pairs?
(1, 42), (2, 21), (3, 14), and (6, 7) are the 42 factors of pairs.

What are the positive factors for 42?
1, 2, 3, 6, 7, 14, 21, and 42 are the positive factors for 42.

What are the negative factors of 42?
-1, -2, -3, -6, -7, -14, -21 and -42 are the negative factors for 42.

We have learned all the required information about the factors of 42. We hope that this article was useful and easy to understand.

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Written by by

Prerit Jain

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