Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a 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 -56, how they are used in real life, and tips for learning them quickly.
The numbers that divide -56 evenly are known as factors of -56.
A factor of -56 is a number that divides the number without remainder.
The factors of -56 are 1, 2, 4, 7, 8, 14, 28, and 56.
Negative factors of -56: -1, -2, -4, -7, -8, -14, -28, and -56.
Prime factors of -56: 2 and 7.
Prime factorization of -56: 23 × 7.
The sum of factors of 56: 1 + 2 + 4 + 7 + 8 + 14 + 28 + 56 = 120
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 -56. Identifying the numbers which are multiplied to get the number -56 is the multiplication method.
Step 1: Multiply -56 by 1, -56 × 1 = -56.
Step 2: Check for other numbers that give -56 after multiplying
-2 × 28 = -56
-4 × 14 = -56
-7 × 8 = -56
Therefore, the positive factor pairs of -56 are: (1, -56), (2, -28), (4, -14), (7, -8).
For every positive factor, there is a negative factor.
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 the simple division method
Step 1: Divide -56 by 1, -56 ÷ 1 = -56.
Step 2: Continue dividing -56 by the numbers until the remainder becomes 0.
-56 ÷ 1 = -56
-56 ÷ 2 = -28
-56 ÷ 4 = -14
-56 ÷ 7 = -8
Therefore, the factors of -56 are: 1, 2, 4, 7, 8, 14, 28, 56.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of -56 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1
The prime factors of -56 are 2 and 7.
The prime factorization of -56 is: 2^3 × 7.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 56 is divided by 2 to get 28.
Step 2: Now divide 28 by 2 to get 14.
Step 3: Then divide 14 by 2 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of -56 is: 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 -56: (1, -56), (2, -28), (4, -14), (7, -8).
Negative factor pairs of -56: (-1, 56), (-2, 28), (-4, 14), (-7, 8).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A teacher has -56 marks to distribute among 7 students equally. How many marks will each student receive?
Each student will receive -8 marks.
To distribute the marks equally, we need to divide the total marks by the number of students.
-56/7 = -8
A field has a length of 14 meters, and the total area is -56 square meters. Find the width.
-4 meters.
To find the width of the field, we use the formula, Area = length × width -56 = 14 × width
To find the value of width, we need to shift 14 to the left side.
-56/14 = width
Width = -4.
There are 28 boxes and -56 items. How many items will be in each box?
Each box will have -2 items.
To find the items in each box, divide the total items by the boxes.
-56/28 = -2
In a class, there are -56 pencils and 8 groups. How many pencils are there in each group?
There are -7 pencils in each group.
Dividing the pencils by the total groups, we will get the number of pencils in each group.
-56/8 = -7
-56 books need to be arranged in 4 shelves. How many books will go on each shelf?
Each of the shelves has -14 books.
Divide total books by shelves.
-56/4 = -14
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.