104 LearnersLast updated on May 26th, 2025
Factors of 288
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 288, how they are used in real life, and tips to learn them quickly.
What are the Factors of 288?
The numbers that divide 288 evenly are known as factors of 288.
A factor of 288 is a number that divides the number without remainder.
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, and 288.
Negative factors of 288: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -48, -72, -96, -144, and -288.
Prime factors of 288: 2 and 3.
Prime factorization of 288: 25 × 32.
The sum of factors of 288: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 32 + 36 + 48 + 72 + 96 + 144 + 288 = 840
How to Find Factors of 288?
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 288. Identifying the numbers which are multiplied to get the number 288 is the multiplication method.
Step 1: Multiply 288 by 1, 288 × 1 = 288.
Step 2: Check for other numbers that give 288 after multiplying
2 × 144 = 288
3 × 96 = 288
4 × 72 = 288
6 × 48 = 288
8 × 36 = 288
9 × 32 = 288
12 × 24 = 288
16 × 18 = 288
Therefore, the positive factor pairs of 288 are: (1, 288), (2, 144), (3, 96), (4, 72), (6, 48), (8, 36), (9, 32), (12, 24), (16, 18).
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 a simple division method -
Step 1: Divide 288 by 1, 288 ÷ 1 = 288.
Step 2: Continue dividing 288 by the numbers until the remainder becomes 0.
288 ÷ 1 = 288
288 ÷ 2 = 144
288 ÷ 3 = 96
288 ÷ 4 = 72
288 ÷ 6 = 48
288 ÷ 8 = 36
288 ÷ 9 = 32
288 ÷ 12 = 24
288 ÷ 16 = 18
Therefore, the factors of 288 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, and 288.
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 288 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
288 ÷ 2 = 144
144 ÷ 2 = 72
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 288 are 2 and 3.
The prime factorization of 288 is: 25 × 32.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 288 is divided by 2 to get 144.
Step 2: Now divide 144 by 2 to get 72.
Step 3: Then divide 72 by 2 to get 36.
Step 4: Divide 36 by 2 to get 18.
Step 5: Divide 18 by 2 to get 9.
Step 6: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 288 is: 25 × 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 288: (1, 288), (2, 144), (3, 96), (4, 72), (6, 48), (8, 36), (9, 32), (12, 24), (16, 18).
Negative factor pairs of 288: (-1, -288), (-2, -144), (-3, -96), (-4, -72), (-6, -48), (-8, -36), (-9, -32), (-12, -24), (-16, -18).
Common Mistakes and How to Avoid Them in Factors of 288
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 288, 1 and 288 are also factors.
Factors of 288 Examples
Problem 1
There are 12 workers and 288 bricks. How will they divide the bricks equally?
They will get 24 bricks each.
Explanation
To divide the bricks equally, we need to divide the total bricks with the number of workers.
288/12 = 24
Problem 2
A garden is rectangular, the length of the garden is 18 meters and the total area is 288 square meters. Find the width?
16 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
288 = 18 × width
To find the value of width, we need to shift 18 to the left side.
288/18 = width
Width = 16.
Problem 3
There are 36 boxes and 288 candies. How many candies will be in each box?
Each box will have 8 candies.
Explanation
To find the candies in each box, divide the total candies with the boxes.
288/36 = 8
Problem 4
In a seminar, there are 288 participants, and 9 groups. How many participants are there in each group?
There are 32 participants in each group.
Explanation
Dividing the participants with the total groups, we will get the number of participants in each group.
288/9 = 32
Problem 5
288 plants need to be arranged in 6 rows. How many plants will go in each row?
Each of the rows has 48 plants.
Explanation
Divide total plants with rows.
288/6 = 48
FAQs on Factors of 288
1.What are the factors of 288?
2.Mention the prime factors of 288.
3.Is 288, a multiple of 9?
4.Mention the factor pairs of 288?
5.What is the square of 288?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 288?
7.What are some fun ways kids in Bahrain can practice Factors of 288 with numbers?
8.What role do numbers and Factors of 288 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 288 skills?
Important Glossaries for Factor of 288
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 288 are 1, 2, 3, 4, 6, 8, 9, etc.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 288.
- 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 288 are (1, 288), (2, 144), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, 288 = 25 × 32.
- Multiplication method: A method used to find the factors by identifying pairs of numbers that multiply to a given number.
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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.
