Factors of 42
2026-02-28 21:40 Diff
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Last updated on December 16, 2025

A number that divides another number exactly without leaving any remainder is called a factor of the given number. Factors play an important role in mathematics and real-life situations. They are useful in deciding the best time to schedule work shifts and events.

What are the Factors of 42

Factors almost often come in pairs. There are several methods to figure them out, which you'll be learning in the following section. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
 

The factors of 42 can be written as shown in the table given below:

Factor Type Values Positive Factors of 42 1, 2, 3, 6, 7, 14, 21, 42 Negative Factors of 42 −1, −2, −3, −6, −7, −14, −21, −42 Prime Factors of 42 2, 3, 2007 Prime Factorization of 42 2 × 3 × 7 The Sum of the Factors of 42 96

How To Find The Factors of 42?

For finding factors, kids can use different methods for easier calculations. A few commonly used methods are as follows:

  • Use of Multiplication Method
  • Use of Division Method
  • Use of Prime Factors and Prime Factorization

So, here we discuss a detailed explanation of the following methods:
 

Finding Factors Using Multiplication Method

In the multiplication method, we will try to find out the numbers that multiply together to give the value, 42, We will check the factors step by step:


Step 1: Start to multiply with numbers, which gives the value of 42.


Start with 1, and continue to multiply with other numbers. 


1 ×  42  = 42
2 ×  21  = 42
3 ×  14  = 42
6 ×  7   = 42


Step 2: After the calculation, we get to these numbers, the factors of 42.


Step 3: The positive factor pairs of 42 found through multiplication are (1, 42), (2, 21), (3, 14), and (6, 7)


Step 4: The negative factor pairs of 274 are (-1, -42), (-2, -21), (-3, -14), and (-6, -7)
 

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Finding Factors Using Division Method

Using this method we will break down the given number till our remainder is zero. Let us go through the step-by-step process to find the factors of 42:


Step 1: Divide 42 by smaller numbers and see if there is any remainder. E.g., 42/1 = 42. 


Step 2: We will continue in the same way and check for other numbers as well. For 42, the factors are 1, 2, 3, 6, 7, 14, 21, and 42. Because 42 can be divided evenly by these numbers.
 

Prime Factors and Prime Factorization

In the prime factorization method, we break down a number into its prime factor. The prime factors of 42 are 2, 3, and 7. The prime factors can be found using the methods given below:


2 is the smallest prime number, so start dividing with two. And then continue to divide with other prime numbers.


42 ÷ 2 =21
21 ÷ 3 = 7
7 ÷ 7 = 1


 The prime factorization of 42 is :


 42= 21 × 31 × 71


With prime factorization, 42 can be broken down into prime factors, 2, 3, and 7.
 

Prime Factors of 42

Prime Factorization of 42

Factor Tree

A factor tree is a graphical representation of breaking a composite number into its prime factors. It is an easy method to find out the factors of any number.


Step 1: 42 divided by 2 gives us the quotient 21.


Step 2: Since 21 is not a prime number, it can be divided further.


42 ÷ 2 =21
21 ÷ 3 = 7
7 ÷ 7 = 1


 The prime factorization of 42 is: 42 = 21 × 31 × 71.

Factor Pairs of 42

The factors of 42 can be written in both positive and negative pairs. The table below represents the factor pairs of 42, where the product of each pair of numbers is equal to 42.

Positive Pair Factors of 42:

Factors Positive Pair Factors 1 × 42 = 42 1, 42 2 × 21 = 42 2, 21 3 × 14 = 42 3, 14 6 × 7 = 42 6, 7

Since the product of two negative numbers is also positive, 42 also has negative pair factors.

Negative Pair Factors of 42:

Factors Negative Pair Factors −1 × −42 = 42 −1, −42 −2 × −21 = 42 −2, −21 −3 × −14 = 42 −3, −14 −6 × −7 = 42 −6, −7

Common Mistakes and How to Avoid Them in Factors Of 42

Children tend to make mistakes while finding the factors of a number. Let us look at how to avoid those mistakes.
 

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Problem 1

A teacher plans to divide 42 students into groups with an equal number of students. If 3 students have each group, how many groups can be formed?

Okay, lets begin

 The total number of groups is 14.
 

Explanation

Yes, the teacher formed 14 groups. The calculation of group formation is to divide the total number of students, by the number of students per group.
42 / 3 =14
 

Well explained 👍

Problem 2

A packet containing 42 candies. How to divide them among 7 children equally?

Okay, lets begin

 Yes, each one will get 2 candies.
 

Explanation

Yes, it can be possible,42 candies can be shared equally with 7 children. Each child will get 2 candies, and nothing will be left.
 

Well explained 👍

Problem 3

Charlie, have a rope. The length of that rope will be 42 cm, when you cut this into equal parts of 2 cm each, calculate how many pieces are there

Okay, lets begin

21 pieces.
 

Explanation

The total length of the rope is 42 cm. If we cut it into 2 cm pieces, we divide 42 by 2. The answer will be 21.
 

Well explained 👍

Problem 4

At a Costco store in Seattle, a manager receives 42 snack boxes to distribute equally among volunteers for a school science fair. The boxes must be divided into equal groups with no leftovers. What are all the possible numbers of volunteers who can receive the snack boxes equally?

Okay, lets begin

1, 2, 3, 6, 7, 14, 21, 42

Explanation

To divide the snack boxes equally with no leftovers, the number of volunteers must be a factor of 42. The factors of 42 are all numbers that divide 42 exactly.

Checking each divisor gives the complete set of possible volunteer counts.

Well explained 👍

Problem 5

An NBA youth training camp is being organized between Chicago and Los Angeles (LA). There are 42 players registered. Coaches want to split the players into equal teams so that each team has the same number of players. Which team sizes are possible for the coaches to use?

Okay, lets begin

1, 2, 3, 6, 7, 14, 21, 42

Explanation

Team sizes must divide 42 evenly so that no players are left out. These possible team sizes are the factors of 42, which represent all the equal ways the players can be grouped.

Well explained 👍

Problem 6

A CVS pharmacy in New York City receives 42 allergy tablets to be packed into equal daily-dose strips for patients during spring season. What are all the possible numbers of tablets that can be placed in each strip?

Okay, lets begin

1, 2, 3, 6, 7, 14, 21, 42

Explanation

Each strip must contain an equal number of tablets with no remainder. The possible strip sizes are determined by the factors of 42, which represent every number that divides 42 exactly.

Well explained 👍

FAQs on Factors of 42

1.What is the largest factor of 42?

 42 is the highest factor. For any number, the highest factor will be that number itself.

2.The highest prime factor of 42?

Prime factors are the prime numbers. For number 42, the highest prime factor is 7.
 

3.How is the prime factorization of 42 expressed?

Prime factorization of 42 is expressed as 21 × 31 × 41
 

4.What is the GCF of 42 and 56?

5.Can 42 be evenly divided by 3?

Yes, it can. 3 is one of the factors of 42, which can be divisible by 42. 
 

6.How many factors does 42 have?

The number 42 has 8 factors. Factors are whole numbers that divide 42 exactly without leaving a remainder. These include both small and large numbers that multiply in pairs to give 42.

7.What is the smallest factor of 42?

The smallest factor of 42 is 1.
This is because 1 divides every whole number evenly, and it is always the smallest possible factor.

8.Which factors of 42 add up to 13?

The factors of 42 that add up to 13 are 6 and 7.
Both numbers divide 42 evenly, and when added together, 6 + 7 = 13.

9.How many even factors does 42 have?

The number 42 has 4 even factors.
Even factors are numbers that are divisible by 2. The even factors of 42 are 2, 6, 14, and 42.

10.What are the odd factors of 42?

The odd factors of 42 are 1, 3, 7, and 21.
Odd factors are numbers that are not divisible by 2 but still divide 42 evenly.

11.What is the sum of all the factors of 42?

The sum of all the factors of 42 is 96.
When you add all the factors: 1, 2, 3, 6, 7, 14, 21, and 42, the total comes to 96.

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.