126 LearnersLast updated on May 26th, 2025
Factors of 3780
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 3780, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3780?
The numbers that divide 3780 evenly are known as factors of 3780.
A factor of 3780 is a number that divides the number without remainder.
The factors of 3780 include 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 63, 75, 90, 126, 150, 180, 189, 252, 315, 378, 630, 945, 1260, 1890, and 3780.
Negative factors of 3780: -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -30, -36, -45, -60, -63, -75, -90, -126, -150, -180, -189, -252, -315, -378, -630, -945, -1260, -1890, and -3780.
Prime factors of 3780: 2, 3, 5, and 7.
Prime factorization of 3780: 2² × 3³ × 5 × 7.
The sum of factors of 3780: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 30 + 36 + 45 + 60 + 63 + 75 + 90 + 126 + 150 + 180 + 189 + 252 + 315 + 378 + 630 + 945 + 1260 + 1890 + 3780 = 11232
How to Find Factors of 3780?
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 3780. Identifying the numbers which are multiplied to get the number 3780 is the multiplication method.
Step 1: Multiply 3780 by 1, 3780 × 1 = 3780.
Step 2: Check for other numbers that give 3780 after multiplying:
2 × 1890 = 3780
3 × 1260 = 3780
4 × 945 = 3780
5 × 756 = 3780
6 × 630 = 3780
Therefore, the positive factor pairs of 3780 are: (1, 3780), (2, 1890), (3, 1260), (4, 945), (5, 756), (6, 630), etc. 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 3780 by 1, 3780 ÷ 1 = 3780.
Step 2: Continue dividing 3780 by the numbers until the remainder becomes 0.
3780 ÷ 1 = 3780
3780 ÷ 2 = 1890
3780 ÷ 3 = 1260
3780 ÷ 4 = 945
3780 ÷ 5 = 756
Therefore, the factors of 3780 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 63, 75, 90, 126, 150, 180, 189, 252, 315, 378, 630, 945, 1260, 1890, and 3780.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 3780 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1
3780 ÷ 2 = 1890
1890 ÷ 2 = 945
945 ÷ 3 = 315
315 ÷ 3 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 3780 are 2, 3, 5, and 7.
The prime factorization of 3780 is: 2² × 3³ × 5 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3780 is divided by 2 to get 1890.
Step 2: Now divide 1890 by 2 to get 945.
Step 3: Then divide 945 by 3 to get 315.
Step 4: Now divide 315 by 3 to get 105.
Step 5: Divide 105 by 3 to get 35.
Step 6: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 3780 is: 2² × 3³ × 5 × 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.
Positive factor pairs of 3780: (1, 3780), (2, 1890), (3, 1260), (4, 945), (5, 756), (6, 630), etc.
Negative factor pairs of 3780: (-1, -3780), (-2, -1890), (-3, -1260), (-4, -945), (-5, -756), (-6, -630), etc.
Common Mistakes and How to Avoid Them in Factors of 3780
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 3780, 1 and 3780 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 3780 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 is a factor because 3780/1.5 = 2520, 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 3780 are prime numbers.
For example, 2, 3, 5, and 7 are the prime factors of 3780, but it has other factors like 4, 9, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking 3780 as 2² × 3³ × 5 × 7 and missing key factors.
Factors of 3780 Examples
Problem 1
A theater has 3780 seats. If there are 630 rows, how many seats are there in each row?
There are 6 seats in each row.
Explanation
To find the number of seats in each row, divide the total seats by the number of rows.
3780/630 = 6
Problem 2
A company has 3780 units of product to distribute equally among 126 teams. How many units will each team receive?
Each team will receive 30 units.
Explanation
To find the units per team, divide the total units by the number of teams.
3780/126 = 30
Problem 3
A farmer has 3780 kg of grain to store in 945 bins. How many kg of grain will each bin hold?
Each bin will hold 4 kg of grain.
Explanation
To find the kg per bin, divide the total kg by the number of bins.
3780/945 = 4
Problem 4
An auditorium has a capacity of 3780 people and 9 sections. How many people can each section accommodate?
Each section can accommodate 420 people.
Explanation
Divide the total capacity by the number of sections to find how many people each section can accommodate.
3780/9 = 420
Problem 5
3780 pages need to be printed, and each printer can print 630 pages. How many printers are needed?
6 printers are needed.
Explanation
Divide the total pages by the pages per printer to find the number of printers needed.
3780/630 = 6
FAQs on Factors of 3780
1.What are the factors of 3780?
2.Mention the prime factors of 3780.
3.Is 3780 a multiple of 18?
4.Mention the factor pairs of 3780.
5.What is the square of 3780?
Important Glossaries for Factors of 3780
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3780 include 1, 2, 3, 4, 5, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 3780.
- 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 3780 include (1, 3780), (2, 1890), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 3780 is 2² × 3³ × 5 × 7.
- Multiples: The result of multiplying a number by an integer. For example, 3780 is a multiple of 1, 2, 3, etc.
Explore More numbers
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.
