Summarize this article:
455 LearnersLast updated on December 16, 2025
Factors of 42
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)
Explore Our Programs
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.
Mistake 1
Confusing Factors with Multiples
The factors of a number can divide the given number without any remainder, whereas multiples are the products of multiplying the number by an integer. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. And the multiples are 12, 24, and 36, etc… To avoid this confusion, always understand the concept separately.
Mistake 2
Ignoring the Negative Factors.
Always remember that each positive factor has a consistent negative factor. For example, factors of 12 are ±1, ±2, ±3, ±4, ±6, ±12.
Mistake 3
Not Checking Divisibility Properly
In some cases, children might wrongly assume that a number cannot be divided further. For example, they may assume that 8 isn't a factor of 24. However, this calculation proves otherwise: 24 ÷ 8 = 3 (no remainder). So 8 is a factor of 24. To avoid this error, always check divisibility.
Mistake 4
Avoiding Larger Factors
Sometimes, students may stop the calculation, after identifying the smaller factors, whereas forget to identify the corresponding larger factors. For example, for the number 24, kids list 1, 2, 3, and 4, and forget the larger factors 6, 8, 12, and 24. The solution to these mistakes is to try to divide numbers systematically, and also pair them with larger factors.
Examples on Factors of 42
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?
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
Problem 2
A packet containing 42 candies. How to divide them among 7 children equally?
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.
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
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.
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?
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.
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?
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.
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?
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.
FAQs on Factors of 42
1.What is the largest factor of 42?
2.The highest prime factor of 42?
3.How is the prime factorization of 42 expressed?
4.What is the GCF of 42 and 56?
5.Can 42 be evenly divided by 3?
6.How many factors does 42 have?
7.What is the smallest factor of 42?
8.Which factors of 42 add up to 13?
9.How many even factors does 42 have?
10.What are the odd factors of 42?
11.What is the sum of all the factors of 42?
Important Terms Related to Factors of 42
- Factors: Factors are numbers that divide a given number exactly, without any remainder. For example, 6 is divisible by 1, 2, 3, and 6. Therefore, 1, 2, 3, and 6 are the factors of 6.
- Prime Factors: Prime factors of the numbers that multiply together to give a certain product. For 42 the prime factors are 2, 3, and 7.
- Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).
More topics related to Factors of 42
![Important Math Links Icon]()
Topics commonly learned together
![Important Math Links Icon]()
Other topics in Factors
![Important Math Links Icon]()
Explore More Numbers Topics
![Important Math Links Icon]()
Numbers category quick links
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.
