Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 42 students and -42 apples. How will they distribute them equally?
Each student will get -1 apple.
To distribute the apples equally, we need to divide the total apples by the number of students.
-42/42 = -1
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.
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.
There are 14 boxes and -42 marbles. How many marbles will be in each box?
Each box will have -3 marbles.
To find the marbles in each box, divide the total marbles by the number of boxes.
-42/14 = -3
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.
Dividing the books by the total shelves, we will get the number of books on each shelf.
-42/3 = -14
42 chairs need to be arranged in 6 rows. How many chairs will go in each row?
Each row will have 7 chairs.
Divide the total chairs by rows.
42/6 = 7
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.
: She loves to read number jokes and games.