122 LearnersLast updated on May 26th, 2025
Factors of -56
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.
What are the Factors of -56?
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
How to Find Factors of -56?
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 -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.
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 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.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 -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.
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of -56
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of -56, 1 and -56 is also a factor.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of -56 consist of -1, -2, -4, 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 -56/1.5 = -37.333, and it 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 -56 are prime numbers.
For example, 2 and 7 are the prime factors of -56, but it has other factors like 4, 14.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -56 as 2^3 × 7 and missing all the key factors.
Factors of -56 Examples
Problem 1
A teacher has -56 marks to distribute among 7 students equally. How many marks will each student receive?
Each student will receive -8 marks.
Explanation
To distribute the marks equally, we need to divide the total marks by the number of students.
-56/7 = -8
Problem 2
A field has a length of 14 meters, and the total area is -56 square meters. Find the width.
-4 meters.
Explanation
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.
Problem 3
There are 28 boxes and -56 items. How many items will be in each box?
Each box will have -2 items.
Explanation
To find the items in each box, divide the total items by the boxes.
-56/28 = -2
Problem 4
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.
Explanation
Dividing the pencils by the total groups, we will get the number of pencils in each group.
-56/8 = -7
Problem 5
-56 books need to be arranged in 4 shelves. How many books will go on each shelf?
Each of the shelves has -14 books.
Explanation
Divide total books by shelves.
-56/4 = -14
FAQs on Factors of -56
1.What are the factors of -56?
2.Mention the prime factors of -56.
3.Is -56 a multiple of 4?
4.Mention the factor pairs of -56.
5.What is the square of -56?
6.How can children in Singapore use numbers in everyday life to understand Factors of -56?
7.What are some fun ways kids in Singapore can practice Factors of -56 with numbers?
8.What role do numbers and Factors of -56 play in helping children in Singapore develop problem-solving skills?
9.How can families in Singapore create number-rich environments to improve Factors of -56 skills?
Important Glossaries for Factor of -56
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -56 are 1, 2, 4, 7, 8, 14, 28, and 56.
- Prime factors: The factors which are prime numbers. For example, 2 and 7 are prime factors of -56.
- 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 -56 are (1, -56), (2, -28), etc.
- Negative factors: Factors can be both positive and negative. For example, -1, -2, -4, etc., are negative factors of -56.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of -56 is 2^3 × 7.
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About BrightChamps in Singapore
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.
