120 LearnersLast updated on May 26th, 2025
Factors of 3300
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 3300, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3300?
The numbers that divide 3300 evenly are known as factors of 3300.
A factor of 3300 is a number that divides the number without remainder.
The factors of 3300 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 25, 30, 33, 44, 50, 55, 60, 66, 75, 100, 110, 132, 150, 165, 220, 300, 330, 550, 660, 825, 1100, 1650, and 3300.
Negative factors of 3300: -1, -2, -3, -4, -5, -6, -10, -11, -12, -15, -20, -22, -25, -30, -33, -44, -50, -55, -60, -66, -75, -100, -110, -132, -150, -165, -220, -300, -330, -550, -660, -825, -1100, -1650, and -3300.
Prime factors of 3300: 2, 3, 5, and 11.
Prime factorization of 3300: 2 × 2 × 3 × 5 × 5 × 11 or 2^2 × 3 × 5^2 × 11.
The sum of factors of 3300: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 11 + 12 + 15 + 20 + 22 + 25 + 30 + 33 + 44 + 50 + 55 + 60 + 66 + 75 + 100 + 110 + 132 + 150 + 165 + 220 + 300 + 330 + 550 + 660 + 825 + 1100 + 1650 + 3300 = 10896
How to Find Factors of 3300?
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 3300. Identifying the numbers which are multiplied to get the number 3300 is the multiplication method.
Step 1: Multiply 3300 by 1, 3300 × 1 = 3300.
Step 2: Check for other numbers that give 3300 after multiplying
2 × 1650 = 3300
3 × 1100 = 3300
4 × 825 = 3300
5 × 660 = 3300
6 × 550 = 3300
10 × 330 = 3300
11 × 300 = 3300
12 × 275 = 3300
15 × 220 = 3300
20 × 165 = 3300
22 × 150 = 3300
25 × 132 = 3300
30 × 110 = 3300
33 × 100 = 3300
44 × 75 = 3300
50 × 66 = 3300
55 × 60 = 3300
Therefore, the positive factor pairs of 3300 are: (1, 3300), (2, 1650), (3, 1100), (4, 825), (5, 660), (6, 550), (10, 330), (11, 300), (12, 275), (15, 220), (20, 165), (22, 150), (25, 132), (30, 110), (33, 100), (44, 75), (50, 66), and (55, 60). All these factor pairs result in 3300. 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 as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 3300 by 1, 3300 ÷ 1 = 3300.
Step 2: Continue dividing 3300 by the numbers until the remainder becomes 0.
3300 ÷ 1 = 3300
3300 ÷ 2 = 1650
3300 ÷ 3 = 1100
3300 ÷ 4 = 825
3300 ÷ 5 = 660
3300 ÷ 6 = 550
3300 ÷ 10 = 330
3300 ÷ 11 = 300
3300 ÷ 12 = 275
3300 ÷ 15 = 220
3300 ÷ 20 = 165
3300 ÷ 22 = 150
3300 ÷ 25 = 132
3300 ÷ 30 = 110
3300 ÷ 33 = 100
3300 ÷ 44 = 75
3300 ÷ 50 = 66
3300 ÷ 55 = 60
Therefore, the factors of 3300 are: 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 25, 30, 33, 44, 50, 55, 60, 66, 75, 100, 110, 132, 150, 165, 220, 300, 330, 550, 660, 825, 1100, 1650, and 3300.
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 3300 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3300 ÷ 2 = 1650
1650 ÷ 2 = 825
825 ÷ 3 = 275
275 ÷ 5 = 55
55 ÷ 5 = 11
11 ÷ 11 = 1
The prime factors of 3300 are 2, 3, 5, and 11.
The prime factorization of 3300 is: 2 × 2 × 3 × 5 × 5 × 11 or 2^2 × 3 × 5^2 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 3300 is divided by 2 to get 1650.
Step 2: Now divide 1650 by 2 to get 825.
Step 3: Then divide 825 by 3 to get 275.
Step 4: Divide 275 by 5 to get 55.
Step 5: Divide 55 by 5 to get 11.
Step 6: Divide 11 by 11 to get 1. Here, 11 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 3300 is: 2 × 2 × 3 × 5 × 5 × 11
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 3300: (1, 3300), (2, 1650), (3, 1100), (4, 825), (5, 660), (6, 550), (10, 330), (11, 300), (12, 275), (15, 220), (20, 165), (22, 150), (25, 132), (30, 110), (33, 100), (44, 75), (50, 66), and (55, 60).
Negative factor pairs of 3300: (-1, -3300), (-2, -1650), (-3, -1100), (-4, -825), (-5, -660), (-6, -550), (-10, -330), (-11, -300), (-12, -275), (-15, -220), (-20, -165), (-22, -150), (-25, -132), (-30, -110), (-33, -100), (-44, -75), (-50, -66), and (-55, -60).
Common Mistakes and How to Avoid Them in Factors of 3300
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 3300, 1 and 3300 are also factors.
Mistake 2
Missing Negative Factors
We tend to mention only positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 3300 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions thinking they are factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor is incorrect, because 3300/1.5 = 2200, 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 3300 are prime numbers is incorrect.
For example, 2, 3, 5, and 11 are the prime factors of 3300, but it has other factors like 4, 10, 100.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3300 as 22 × 3 × 52 × 11 and missing all the key factors.
Factors of 3300 Examples
Problem 1
There are 11 teams and 3300 tickets. How will they divide them equally?
They will get 300 tickets each.
Explanation
To divide the tickets equally, we need to divide the total tickets by the number of teams.
3300/11 = 300
Problem 2
A field is rectangular, the length of the field is 25 meters and the total area is 3300 square meters. Find the width?
132 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
3300 = 25 × width
To find the value of width, we need to divide 3300 by 25.
3300/25 = width
Width = 132.
Problem 3
There are 55 buses and 3300 passengers. How many passengers will be in each bus?
Each bus will have 60 passengers.
Explanation
To find the passengers in each bus, divide the total passengers by the number of buses.
3300/55 = 60
Problem 4
In a factory, there are 1100 workers and 3 departments. How many workers are there in each department?
There are 366 workers in each department.
Explanation
Dividing the workers by the total departments, we will get the number of workers in each department.
1100/3 = 366 (rounded down to the nearest whole number).
Problem 5
3300 chairs need to be arranged in 6 rows. How many chairs will go in each row?
Each row will have 550 chairs.
Explanation
Divide total chairs by rows.
3300/6 = 550
FAQs on Factors of 3300
1.What are the factors of 3300?
2.Mention the prime factors of 3300.
3.Is 3300 a multiple of 11?
4.Mention the factor pairs of 3300?
5.What is the square of 3300?
6.How can children in Qatar use numbers in everyday life to understand Factors of 3300?
7.What are some fun ways kids in Qatar can practice Factors of 3300 with numbers?
8.What role do numbers and Factors of 3300 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 3300 skills?
Important Glossaries for Factor of 3300
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3300 are 1, 2, 3, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 11 are prime factors of 3300.
- 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 3300 are (1, 3300), (2, 1650), etc.
- Prime factorization: Breaking down a number into its prime factor components. For example, the prime factorization of 3300 is 22 × 3 × 52 × 11.
- Multiple: A multiple of a number is the product of that number and an integer. For example, 3300 is a multiple of 11.
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About BrightChamps in Qatar
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.
