Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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.
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To find the number of seats in each row, divide the total seats by the number of rows.
3780/630 = 6
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.
To find the units per team, divide the total units by the number of teams.
3780/126 = 30
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.
To find the kg per bin, divide the total kg by the number of bins.
3780/945 = 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.
Divide the total capacity by the number of sections to find how many people each section can accommodate.
3780/9 = 420
3780 pages need to be printed, and each printer can print 630 pages. How many printers are needed?
6 printers are needed.
Divide the total pages by the pages per printer to find the number of printers needed.
3780/630 = 6
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.
: She loves to read number jokes and games.