113 LearnersLast updated on May 26th, 2025
Factors of 3900
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.
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
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
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.
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.
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.
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).
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
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 3900, 1 and 3900 is also a factor.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 3900 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor
For example, thinking 1.5 as a factor, because 3900/1.5 = 2600, 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 3900 are prime numbers. For example, 2, 3, 5, and 13 are the prime factors of 3900, but it has other factors like 6, 10, 39, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3900 as 2² × 3 × 5² × 13 and missing all the key factors.
Factors of 3900 Examples
Problem 1
There are 39 teams in a sports meet and 3900 water bottles. How many bottles will each team get if distributed equally?
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
Problem 2
A rectangular garden has an area of 3900 square meters, and the length is 65 meters. Find the width of the garden.
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.
Problem 3
There are 78 students and 3900 pencils. How many pencils will each student get?
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
Problem 4
A bakery produces 3900 loaves of bread and packs them into boxes containing 30 loaves each. How many boxes will they fill?
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
Problem 5
An auditorium has 15 rows of seats. If there are a total of 3900 seats, how many seats are in each row?
Each row has 260 seats.
Explanation
Divide the total number of seats by the number of rows.
3900/15 = 260
FAQs on Factors of 3900
1.What are the factors of 3900?
2.Mention the prime factors of 3900.
3.Is 3900 a multiple of 13?
4.Mention the factor pairs of 3900?
5.What is the square of 3900?
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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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.
