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Last updated on May 26th, 2025

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Factors of 3900

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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 3900, how they are used in real life, and tips to learn them quickly.

Factors of 3900 for Australian Students
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What are the Factors of 3900?

The numbers that divide 3900 evenly are known as factors of 3900.

 

A factor of 3900 is a number that divides the number without remainder.

 

The factors of 3900 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 650, 780, 975, 1300, 1950, and 3900.

 

Negative factors of 3900 include: -1, -2, -3, -4, -5, -6, -10, -12, -13, -15, -20, -26, -30, -39, -52, -60, -65, -78, -130, -156, -195, -260, -390, -650, -780, -975, -1300, -1950, and -3900.

 

Prime factors of 3900: 2, 3, 5, and 13.

 

Prime factorization of 3900: 2² × 3 × 5² × 13.

 

The sum of factors of 3900: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 13 + 15 + 20 + 26 + 30 + 39 + 52 + 60 + 65 + 78 + 130 + 156 + 195 + 260 + 390 + 650 + 780 + 975 + 1300 + 1950 + 3900 = 12402

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How to Find Factors of 3900?

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
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 3900. Identifying the numbers which are multiplied to get the number 3900 is the multiplication method.

 

Step 1: Multiply 3900 by 1, 3900 × 1 = 3900.

 

Step 2: Check for other numbers that give 3900 after multiplying

2 × 1950 = 3900

3 × 1300 = 3900

4 × 975 = 3900

5 × 780 = 3900

6 × 650 = 3900

10 × 390 = 3900

12 × 325 = 3900

13 × 300 = 3900

15 × 260 = 3900

20 × 195 = 3900

26 × 150 = 3900

30 × 130 = 3900

39 × 100 = 3900

52 × 75 = 3900

60 × 65 = 3900

 

Therefore, the positive factor pairs of 3900 are: (1, 3900), (2, 1950), (3, 1300), (4, 975), (5, 780), (6, 650), (10, 390), (12, 325), (13, 300), (15, 260), (20, 195), (26, 150), (30, 130), (39, 100), (52, 75), (60, 65). For every positive factor, there is a negative factor.

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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 a whole number as factors. Factors can be calculated by following a simple division method -

 

Step 1: Divide 3900 by 1, 3900 ÷ 1 = 3900.

 

Step 2: Continue dividing 3900 by the numbers until the remainder becomes 0.

3900 ÷ 1 = 3900

3900 ÷ 2 = 1950

3900 ÷ 3 = 1300

3900 ÷ 4 = 975

3900 ÷ 5 = 780

3900 ÷ 6 = 650

3900 ÷ 10 = 390

3900 ÷ 12 = 325

3900 ÷ 13 = 300

3900 ÷ 15 = 260

3900 ÷ 20 = 195

3900 ÷ 26 = 150

3900 ÷ 30 = 130

3900 ÷ 39 = 100

3900 ÷ 52 = 75

3900 ÷ 60 = 65

 

Therefore, the factors of 3900 are: 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 650, 780, 975, 1300, 1950, 3900.

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Prime Factors and Prime Factorization

The factors can be found by dividing 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 3900 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

3900 ÷ 2 = 1950

1950 ÷ 2 = 975

975 ÷ 3 = 325

325 ÷ 5 = 65

65 ÷ 5 = 13

13 ÷ 13 = 1

 

The prime factors of 3900 are 2, 3, 5, and 13.

 

The prime factorization of 3900 is: 2² × 3 × 5² × 13.

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Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

 

Step 1: Firstly, 3900 is divided by 2 to get 1950.

 

Step 2: Now divide 1950 by 2 to get 975.

 

Step 3: Then divide 975 by 3 to get 325.

 

Step 4: Divide 325 by 5 to get 65.

 

Step 5: Finally, divide 65 by 5 to get 13. Here, 13 is a prime number, that cannot be divided anymore. So, the prime factorization of 3900 is: 2² × 3 × 5² × 13.

 

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 3900: (1, 3900), (2, 1950), (3, 1300), (4, 975), (5, 780), (6, 650), (10, 390), (12, 325), (13, 300), (15, 260), (20, 195), (26, 150), (30, 130), (39, 100), (52, 75), (60, 65).

 

Negative factor pairs of 3900: (-1, -3900), (-2, -1950), (-3, -1300), (-4, -975), (-5, -780), (-6, -650), (-10, -390), (-12, -325), (-13, -300), (-15, -260), (-20, -195), (-26, -150), (-30, -130), (-39, -100), (-52, -75), (-60, -65).

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Common Mistakes and How to Avoid Them in Factors of 3900

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

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Forgetting the number itself and 1 is a factor

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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 3900, 1 and 3900 is also a factor.

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Factors of 3900 Examples

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Problem 1

There are 39 teams in a sports meet and 3900 water bottles. How many bottles will each team get if distributed equally?

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Each team will get 100 bottles.

Explanation

To distribute the bottles equally, we need to divide the total bottles by the number of teams.

 

3900/39 = 100

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Problem 2

A rectangular garden has an area of 3900 square meters, and the length is 65 meters. Find the width of the garden.

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60 meters.

Explanation

To find the width of the garden, we use the formula,

 

Area = length × width

 

3900 = 65 × width

 

To find the value of width, we need to shift 65 to the left side.

 

3900/65 = width

 

Width = 60.

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Problem 3

There are 78 students and 3900 pencils. How many pencils will each student get?

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Each student will get 50 pencils.

Explanation

To find the pencils each student will get, divide the total pencils by the number of students.

 

3900/78 = 50

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Problem 4

A bakery produces 3900 loaves of bread and packs them into boxes containing 30 loaves each. How many boxes will they fill?

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They will fill 130 boxes.

Explanation

Dividing the total loaves by the number of loaves per box, we get the number of boxes.

 

3900/30 = 130

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Problem 5

An auditorium has 15 rows of seats. If there are a total of 3900 seats, how many seats are in each row?

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Each row has 260 seats.

Explanation

Divide the total number of seats by the number of rows.

 

3900/15 = 260

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FAQs on Factors of 3900

1.What are the factors of 3900?

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2.Mention the prime factors of 3900.

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3.Is 3900 a multiple of 13?

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4.Mention the factor pairs of 3900?

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5.What is the square of 3900?

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6.How can children in Australia use numbers in everyday life to understand Factors of 3900?

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7.What are some fun ways kids in Australia can practice Factors of 3900 with numbers?

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8.What role do numbers and Factors of 3900 play in helping children in Australia develop problem-solving skills?

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9.How can families in Australia create number-rich environments to improve Factors of 3900 skills?

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Important Glossaries for Factors of 3900

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3900 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 650, 780, 975, 1300, 1950, and 3900.

 

  • Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 13 are prime factors of 3900.

 

  • 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 3900 are (1, 3900), (2, 1950), etc.

 

  • Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 3900 is 2² × 3 × 5² × 13.

 

  • Multiplication method: A method used to find factors by identifying pairs of numbers that multiply to give the original number. For example, 2 × 1950 = 3900 is a multiplication method used to find factors of 3900.
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About BrightChamps in Australia

At BrightChamps, numbers mean more than just digits—they open doors to a world of possibilities! We’re here to help children across Australia grasp essential math skills, focusing today on Factors of 3900 with a special emphasis on factors—in a way that’s fun, engaging, and easy to follow. Whether your child is figuring out the speed of a roller coaster at Luna Park Sydney, keeping score at a local cricket match, or managing their allowance to buy gadgets, understanding numbers builds everyday confidence. Our hands-on lessons make learning enjoyable and straightforward. Since kids in Australia learn differently, we customize lessons to suit each child’s style. From Sydney’s vibrant streets to the beautiful Gold Coast beaches, BrightChamps brings math to life throughout Australia. Let’s make factors an exciting part of every child’s math journey!
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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.

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Fun Fact

: She loves to read number jokes and games.

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