122 LearnersLast updated on May 26th, 2025
Factors of -144
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 -144, how they are used in real life, and tips to learn them quickly.
What are the Factors of -144?
The numbers that divide -144 evenly are known as factors of -144.
A factor of -144 is a number that divides the number without a remainder.
The factors of -144 include both positive and negative numbers: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144, and their negatives: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72, -144.
Prime factors of 144: 2 and 3.
Prime factorization of 144: 24 × 32.
The sum of the positive factors of 144: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 36 + 48 + 72 + 144 = 403
How to Find Factors of -144?
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 pairs of numbers that are multiplied to give 144. Identifying the numbers that are multiplied to get the number 144 is the multiplication method.
Step 1: Multiply 144 by 1, 144 × 1 = 144.
Step 2: Check for other numbers that give 144 after multiplying
2 × 72 = 144
3 × 48 = 144
4 × 36 = 144
6 × 24 = 144
8 × 18 = 144
9 × 16 = 144
12 × 12 = 144
Therefore, the positive factor pairs of 144 are: (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), (12, 12).
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 144 by 1, 144 ÷ 1 = 144.
Step 2: Continue dividing 144 by the numbers until the remainder becomes 0.
144 ÷ 1 = 144
144 ÷ 2 = 72
144 ÷ 3 = 48
144 ÷ 4 = 36
144 ÷ 6 = 24
144 ÷ 8 = 18
144 ÷ 9 = 16
144 ÷ 12 = 12
Therefore, the factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
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 144 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
144 ÷ 2 = 72
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 144 are 2 and 3.
The prime factorization of 144 is: 2^4 × 3^2.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 144 is divided by 2 to get 72.
Step 2: Now divide 72 by 2 to get 36.
Step 3: Then divide 36 by 2 to get 18.
Step 4: Divide 18 by 2 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 144 is: 24 × 32.
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 144: (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), and (12, 12).
Negative factor pairs of 144: (-1, -144), (-2, -72), (-3, -48), (-4, -36), (-6, -24), (-8, -18), (-9, -16), and (-12, -12).
Common Mistakes and How to Avoid Them in Factors of -144
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 -144, 1 and 144 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 -144 include -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 144/1.5 = 96, 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 144 are prime numbers.
For example, 2 and 3 are the prime factors of 144, but it has other factors like 4, 9.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 144 as 2^4 × 3^2 and missing all the key factors.
Factors of -144 Examples
Problem 1
There are 9 teams and 144 points to distribute. How will they divide it equally?
Each team will get 16 points.
Explanation
To divide the points equally, we need to divide the total points with the number of teams.
144/9 = 16
Problem 2
A room is rectangular, the length of the room is 12 meters and the total area is 144 square meters. Find the width.
12 meters.
Explanation
To find the width of the room, we use the formula,
Area = length × width
144 = 12 × width
To find the value of the width, we need to divide 144 by 12.
144/12 = width
Width = 12.
Problem 3
There are 18 boxes and 144 apples. How many apples will be in each box?
Each box will have 8 apples.
Explanation
To find the apples in each box, divide the total apples with the boxes.
144/18 = 8
Problem 4
In a school, there are 144 students, and 6 buses. How many students are there in each bus?
There are 24 students in each bus.
Explanation
Dividing the students by the total buses, we will get the number of students in each bus.
144/6 = 24
Problem 5
144 books need to be arranged in 12 shelves. How many books will go on each shelf?
Each of the shelves has 12 books.
Explanation
Divide the total books by shelves.
144/12 = 12
FAQs on Factors of -144
1.What are the factors of -144?
2.Mention the prime factors of -144.
3.Is 144 a multiple of 12?
4.Mention the factor pairs of -144?
5.What is the square root of 144?
6.How can children in Canada use numbers in everyday life to understand Factors of -144?
7.What are some fun ways kids in Canada can practice Factors of -144 with numbers?
8.What role do numbers and Factors of -144 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of -144 skills?
Important Glossaries for Factor of -144
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 144.
- 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 144 are (1, 144), (2, 72), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, 144 is 24 × 32.
- Multiplication method: A way to find factors by identifying pairs of numbers that multiply to the target number.
Explore More numbers
About BrightChamps in Canada
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.
