115 LearnersLast updated on May 26th, 2025
Factors of 33600
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 33600, how they are used in real life, and tips to learn them quickly.
What are the Factors of 33600?
The numbers that divide 33600 evenly are known as factors of 33600.
A factor of 33600 is a number that divides the number without remainder.
The positive factors of 33600 include 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 70, 80, 84, 96, 105, 112, 120, 140, 168, 175, 210, 224, 240, 280, 336, 420, 480, 560, 672, 840, 1050, 1120, 1344, 1680, 2100, 3360, 4200, 5600, 6720, 8400, 11200, 16800, and 33600.
Negative factors of 33600 are the negatives of all the positive factors.
Prime factors of 33600: 2, 3, 5, and 7.
Prime factorization of 33600: 26 × 3 × 52 × 7.
The sum of factors of 33600 is a detailed calculation that involves adding up all the factors listed above.
How to Find Factors of 33600?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using 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 33600. Identifying the numbers which are multiplied to get the number 33600 is the multiplication method. Example factor pairs include:
33600 × 1 = 33600
16800 × 2 = 33600
11200 × 3 = 33600
8400 × 4 = 33600
6720 × 5 = 33600
5600 × 6 = 33600
4800 × 7 = 33600
4200 × 8 = 33600 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 the numbers that result as whole numbers as factors. Factors can be calculated using a simple division method - Example steps: 33600 ÷ 1 = 33600
33600 ÷ 2 = 16800
33600 ÷ 3 = 11200
33600 ÷ 4 = 8400
33600 ÷ 5 = 6720
33600 ÷ 6 = 5600
33600 ÷ 7 = 4800
Therefore, the factors of 33600 include 1, 2, 3, 4, 5, 6, 7, 8, 10, and many more.
Prime Factors and Prime Factorization
The factors can be found by dividing the number by prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using a factor tree
Using Prime Factorization: In this process, prime factors of 33600 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
33600 ÷ 2 = 16800
16800 ÷ 2 = 8400
8400 ÷ 2 = 4200
4200 ÷ 2 = 2100
2100 ÷ 2 = 1050
1050 ÷ 2 = 525
525 ÷ 3 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 33600 are 2, 3, 5, and 7.
The prime factorization of 33600 is: 26 × 3 × 52 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 33600 is divided by 2 to get 16800.
Step 2: Divide 16800 by 2 to get 8400.
Step 3: Then divide 8400 by 2 to get 4200.
Step 4: Continue dividing by 2 until no longer possible, then use 3, 5, and finally 7. So, the prime factorization of 33600 is: 26 × 3 × 52 × 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.
Example positive factor pairs of 33600: (1, 33600), (2, 16800), (3, 11200), (4, 8400), and so on.
Example negative factor pairs of 33600: (-1, -33600), (-2, -16800), (-3, -11200), (-4, -8400), and so on.
Common Mistakes and How to Avoid Them in Factors of 33600
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 as 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 word. Always remember to include 1 and the number itself.
For example, in factors of 33600, 1 and 33600 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 33600 consist of -1, -2, -3, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 33600/1.5 = 22400, which is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only primes.
For example, thinking all the factors of 33600 are prime numbers. For example, 2, 3, 5, and 7 are the prime factors of 33600, but it has other factors like 4, 10, 6720, etc.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 33600 as 2^6 × 3 × 5^2 × 7 and missing all the key factors.
Factors of 33600 Examples
Problem 1
There are 336 students and 33600 candies. How will they divide it equally?
They will get 100 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
33600/336 = 100
Problem 2
A field is rectangular, the length of the field is 140 meters, and the total area is 33600 square meters. Find the width.
240 meters.
Explanation
To find the width of the field, we use the formula:
Area = length × width
33600 = 140 × width
To find the width, we shift 140 to the left side.
33600/140 = width
Width = 240.
Problem 3
There are 56 bags and 33600 apples. How many apples will be in each bag?
Each bag will have 600 apples.
Explanation
To find the apples in each bag, divide the total apples by the number of bags.
33600/56 = 600
Problem 4
In a class, there are 336 students, and 7 groups. How many students are there in each group?
There are 48 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
336/7 = 48
Problem 5
33600 books need to be arranged in 240 shelves. How many books will go on each shelf?
Each shelf will have 140 books.
Explanation
Divide total books by shelves.
33600/240 = 140
FAQs on Factors of 33600
1.What are the factors of 33600?
2.Mention the prime factors of 33600.
3.Is 33600 a multiple of 8?
4.Mention the factor pairs of 33600?
5.What is the square of 33600?
Important Glossaries for Factors of 33600
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 33600 include 1, 2, 3, 4, 5, and more.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 33600.
- 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 33600 include (1, 33600), (2, 16800), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 33600 is 26 × 3 × 52 × 7.
- Division method: A method to find factors by dividing the number by whole numbers until the remainder is zero.
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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.
