100 LearnersLast updated on May 26th, 2025
Factors of 9600
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 9600, how they are used in real life, and tips to learn them quickly.
What are the Factors of 9600?
The numbers that divide 9600 evenly are known as factors of 9600.
A factor of 9600 is a number that divides the number without remainder.
The factors of 9600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, and 9600.
Negative factors of 9600: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -32, -40, -48, -60, -64, -80, -96, -120, -160, -192, -240, -320, -480, -9600.
Prime factors of 9600: 2, 3, and 5. Prime factorization of 9600: 27 × 3 × 52.
The sum of factors of 9600 is a lengthy calculation, given the number of factors, and is typically calculated with advanced tools.
How to Find Factors of 9600?
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 9600. Identifying the numbers which are multiplied to get the number 9600 is the multiplication method.
Step 1: Multiply 9600 by 1, 9600 × 1 = 9600.
Step 2: Check for other numbers that give 9600 after multiplying
2 × 4800 = 9600
3 × 3200 = 9600
5 × 1920 = 9600
10 × 960 = 9600
Therefore, the positive factor pairs of 9600 include: (1, 9600), (2, 4800), (3, 3200), (4, 2400), (5, 1920), (6, 1600), (8, 1200), (10, 960), (12, 800), (15, 640), (16, 600), (20, 480), (24, 400), (30, 320), (32, 300), (40, 240), (48, 200), (60, 160), (64, 150), (80, 120), and so on.
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 9600 by 1, 9600 ÷ 1 = 9600.
Step 2: Continue dividing 9600 by the numbers until the remainder becomes 0.
9600 ÷ 1 = 9600
9600 ÷ 2 = 4800
9600 ÷ 3 = 3200
9600 ÷ 4 = 2400
9600 ÷ 5 = 1920
Therefore, the factors of 9600 are numerous and include: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960, 1920, 2400, 3200, 4800, 9600.
Prime Factors and Prime Factorization
The factors can be found by dividing by 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 9600 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
9600 ÷ 2 = 4800
4800 ÷ 2 = 2400
2400 ÷ 2 = 1200
1200 ÷ 2 = 600
600 ÷ 2 = 300
300 ÷ 2 = 150
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 9600 are 2, 3, and 5.
The prime factorization of 9600 is: 27 × 3 × 52.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 9600 is divided by 2 to get 4800.
Step 2: Now divide 4800 by 2 to get 2400.
Step 3: Then divide 2400 by 2 to get 1200.
Step 4: Continue dividing by 2 till you reach 75, which is then divided by 3, and then by 5.
Here, 5 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 9600 is: 27 × 3 × 52.
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 9600: (1, 9600), (2, 4800), (3, 3200), (4, 2400), (5, 1920), (6, 1600), (8, 1200), (10, 960), (12, 800), (15, 640), (16, 600), (20, 480), (24, 400), (30, 320), (32, 300), (40, 240), (48, 200), (60, 160), (64, 150), (80, 120).
Negative factor pairs of 9600: (-1, -9600), (-2, -4800), (-3, -3200), (-4, -2400), (-5, -1920), (-6, -1600), (-8, -1200), (-10, -960), (-12, -800), (-15, -640), (-16, -600), (-20, -480), (-24, -400), (-30, -320), (-32, -300), (-40, -240), (-48, -200), (-60, -160), (-64, -150), (-80, -120).
Common Mistakes and How to Avoid Them in Factors of 9600
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 word. Always remember to include 1 and the number itself.
For example, in factors of 9600, 1 and 9600 are also factors.
Factors of 9600 Examples
Problem 1
There is a company that needs to distribute 9600 leaflets equally among 8 employees. How many leaflets will each employee get?
Each employee will get 1200 leaflets.
Explanation
To distribute the leaflets equally, we need to divide the total leaflets by the number of employees.
9600/8 = 1200
Problem 2
A garden has an area of 9600 square meters. If the garden is rectangular and the length is 80 meters, what is the width?
120 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
9600 = 80 × width
To find the value of the width, we need to shift 80 to the left side.
9600/80 = width
Width = 120.
Problem 3
There are 60 boxes and 9600 candies. How many candies will be in each box?
Each box will have 160 candies.
Explanation
To find the candies in each box, divide the total candies by the number of boxes.
9600/60 = 160
Problem 4
In a hotel, there are 9600 guests, and the hotel has 64 rooms. How many guests can be accommodated per room?
There are 150 guests in each room.
Explanation
Dividing the guests by the total rooms, we will get the number of guests in each room.
9600/64 = 150
Problem 5
9600 apples need to be packed in 80 crates. How many apples will go in each crate?
Each crate will contain 120 apples.
Explanation
Divide the total apples by the number of crates.
9600/80 = 120
FAQs on Factors of 9600
1.What are the factors of 9600?
2.Mention the prime factors of 9600.
3.Is 9600 a multiple of 6?
4.Mention the factor pairs of 9600?
5.What is the square of 9600?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 9600?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 9600 with numbers?
8.What role do numbers and Factors of 9600 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 9600 skills?
Important Glossaries for Factor of 9600
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 9600 are numerous and include 1, 2, 3, 4, 5, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 9600.
- Prime factorization: The process of breaking down a number into the product of its prime factors. For example, the prime factorization of 9600 is 27 × 3 × 52.
- 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 9600 are (1, 9600), (2, 4800), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using multiplication to find factors of 9600.
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About BrightChamps in United Arab Emirates
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.
