129 LearnersLast updated on May 26th, 2025
Factors of -42
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of -42, how they are used in real life, and tips to learn them quickly.
What are the Factors of -42?
The numbers that divide -42 evenly are known as factors of -42.
A factor of -42 is a number that divides the number without remainder.
The factors of -42 are 1, 2, 3, 6, 7, 14, 21, and 42.
Negative factors of -42: -1, -2, -3, -6, -7, -14, -21, and -42.
Prime factors of -42: 2, 3, and 7.
Prime factorization of -42: -1 × 2 × 3 × 7.
The sum of positive factors of 42: 1 + 2 + 3 + 6 + 7 + 14 + 21 + 42 = 96
How to Find Factors of -42?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the division method
- Prime factors and prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give -42. Identifying the numbers which are multiplied to get the number -42 is the multiplication method.
Step 1: Multiply -42 by 1, -42 × 1 = -42.
Step 2: Check for other numbers that give -42 after multiplying 2 × -21 = -42
3 × -14 = -42
6 × -7 = -42
Therefore, the positive factor pairs of -42 are: (1, -42), (2, -21), (3, -14), (6, -7).
For every positive factor, there is a negative factor pair.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide -42 by 1, -42 ÷ 1 = -42.
Step 2: Continue dividing -42 by the numbers until the remainder becomes 0.
-42 ÷ 1 = -42
-42 ÷ 2 = -21
-42 ÷ 3 = -14
-42 ÷ 6 = -7
Therefore, the factors of -42 are: 1, 2, 3, 6, 7, 14, 21, and 42.
Prime Factors and Prime Factorization
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of -42 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of -42 are 2, 3, and 7.
The prime factorization of -42 is: -1 × 2 × 3 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, -42 is divided by 2 to get -21.
Step 2: Now divide -21 by 3 to get -7.
Step 3: Here, -7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of -42 is: -1 × 2 × 3 × 7.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of -42: (1, -42), (2, -21), (3, -14), and (6, -7).
Negative factor pairs of -42: (-1, 42), (-2, 21), (-3, 14), and (-6, 7).
Common Mistakes and How to Avoid Them in Factors of -42
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of -42, 1 and -42 are also factors.
Mistake 2
Missing Negative Factors
We have used to mention only positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of -42 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because -42/1.5 = -28, which is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes. For example, thinking all the factors of -42 are prime numbers.
For example, 2, 3, and 7 are the prime factors of -42, but it has other factors like 6, 14.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -42 as -1 × 2 × 3 × 7 and missing all the key factors.
Factors of -42 Examples
Problem 1
There are 42 students and -42 apples. How will they distribute them equally?
Each student will get -1 apple.
Explanation
To distribute the apples equally, we need to divide the total apples by the number of students.
-42/42 = -1
Problem 2
A field is rectangular, the width of the field is 7 meters, and the total area is -42 square meters. Find the length?
-6 meters.
Explanation
To find the length of the field, we use the formula, Area = length × width
-42 = length × 7
To find the value of length, we need to shift 7 to the left side.
-42/7 = length
Length = -6.
Problem 3
There are 14 boxes and -42 marbles. How many marbles will be in each box?
Each box will have -3 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
-42/14 = -3
Problem 4
In a class, there are -42 books and 3 shelves. How many books are there on each shelf?
There are -14 books on each shelf.
Explanation
Dividing the books by the total shelves, we will get the number of books on each shelf.
-42/3 = -14
Problem 5
42 chairs need to be arranged in 6 rows. How many chairs will go in each row?
Each row will have 7 chairs.
Explanation
Divide the total chairs by rows.
42/6 = 7
FAQs on Factors of -42
1.What are the factors of -42?
2.Mention the prime factors of -42.
3.Is -42 a multiple of 7?
4.Mention the factor pairs of -42?
5.What is the square of -42?
6.How can children in United States use numbers in everyday life to understand Factors of -42?
7.What are some fun ways kids in United States can practice Factors of -42 with numbers?
8.What role do numbers and Factors of -42 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of -42 skills?
Important Glossaries for Factor of -42
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -42 are 1, 2, 3, 6, 7, 14, 21, and 42.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of -42.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of -42 are (1, -42), (2, -21), etc.
- Negative factors: Factors that are negative, meaning when multiplied they give the original negative number. For example, -1, -2, -3, etc., are negative factors of -42.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of -42 is -1 × 2 × 3 × 7.
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About BrightChamps in United States
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.
