120 LearnersLast updated on May 26th, 2025
Factors of -216
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 -216, how they are used in real life, and tips to learn them quickly.
What are the Factors of -216?
The numbers that divide -216 evenly are known as factors of -216.
A factor of -216 is a number that divides the number without remainder.
The factors of -216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
Negative factors of -216: -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -108, and -216.
Prime factors of -216: 2 and 3.
Prime factorization of -216: -1 × 23 × 33.
The sum of the positive factors of 216: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 108 + 216 = 600
How to Find Factors of -216?
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 216. Identifying the numbers which are multiplied to get the number 216 is the multiplication method.
Step 1: Multiply -216 by -1, -216 × -1 = 216.
Step 2: Check for other numbers that give 216 after multiplying
2 × 108 = 216
3 × 72 = 216
4 × 54 = 216
6 × 36 = 216
8 × 27 = 216
9 × 24 = 216
12 × 18 = 216
Therefore, the positive factor pairs of 216 are: (1, 216), (2, 108), (3, 72), (4, 54), (6, 36), (8, 27), (9, 24), (12, 18).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide -216 by -1, -216 ÷ -1 = 216.
Step 2: Continue dividing 216 by the numbers until the remainder becomes 0.
216 ÷ 1 = 216
216 ÷ 2 = 108
216 ÷ 3 = 72
216 ÷ 4 = 54
216 ÷ 6 = 36
216 ÷ 8 = 27
216 ÷ 9 = 24
216 ÷ 12 = 18
Therefore, the factors of 216 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.
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 -216 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
216 ÷ 2 = 108
108 ÷ 2 = 54
54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of -216 are 2 and 3.
The prime factorization of -216 is: -1 × 2^3 × 3^3.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 216 is divided by 2 to get 108.
Step 2: Now divide 108 by 2 to get 54.
Step 3: Then divide 54 by 2 to get 27.
Step 4: Divide 27 by 3 to get 9.
Step 5: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number that cannot be divided anymore. So, the prime factorization of -216 is: -1 × 23 × 33.
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 216: (1, 216), (2, 108), (3, 72), (4, 54), (6, 36), (8, 27), (9, 24), (12, 18).
Negative factor pairs of -216: (-1, -216), (-2, -108), (-3, -72), (-4, -54), (-6, -36), (-8, -27), (-9, -24), (-12, -18).
Common Mistakes and How to Avoid Them in Factors of -216
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 -216, 1 and 216 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of -216 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 216/1.5 = 144, 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 216 are prime numbers.
For example, 2 and 3 are the prime factors of 216, but it has other factors like 4, 12.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing the wrong factors.
For example, not breaking -216 as -1 × 2^3 × 3^3 and missing all the key factors.
Factors of -216 Examples
Problem 1
There are 12 boxes and -216 marbles. How will they divide them equally?
They will get -18 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of boxes.
-216/12 = -18
Problem 2
A rectangular water tank has a length of 18 meters and a total volume of 216 cubic meters. Find the width if the height is 2 meters.
6 meters.
Explanation
To find the width of the tank, we use the formula,
Volume = length × width × height
216 = 18 × width × 2
To find the value of width, we need to shift 18 and 2 to the left side.
216/(18 × 2) = width
Width = 6.
Problem 3
There are 27 crates and -216 apples. How many apples will be in each crate?
Each crate will have -8 apples.
Explanation
To find the apples in each crate, divide the total apples by the number of crates.
-216/27 = -8
Problem 4
In a class, there are 36 students and 216 candies. How many candies are there for each student?
There are 6 candies per student.
Explanation
Dividing the candies by the total number of students, we will get the number of candies for each student.
216/36 = 6
Problem 5
216 books need to be arranged on 9 shelves. How many books will go on each shelf?
Each of the shelves has 24 books.
Explanation
Divide total books by the number of shelves.
216/9 = 24
FAQs on Factors of -216
1.What are the factors of -216?
2.Mention the prime factors of -216.
3.Is -216 a multiple of 4?
4.Mention the factor pairs of -216?
5.What is the cube root of -216?
6.How can children in Bahrain use numbers in everyday life to understand Factors of -216?
7.What are some fun ways kids in Bahrain can practice Factors of -216 with numbers?
8.What role do numbers and Factors of -216 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of -216 skills?
Important Glossaries for Factors of -216
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of -216.
- Negative factors: The factors that are negative. For example, -1, -2, -3, -4, etc., are negative factors of -216.
- 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 216 are (1, 216), (2, 108), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of -216 is -1 × 2^3 × 3^3.
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About BrightChamps in Bahrain
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.
