Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a 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 3630, how they are used in real life, and the tips to learn them quickly.
The numbers that divide 3630 evenly are known as factors of 3630.
A factor of 3630 is a number that divides the number without a remainder.
The factors of 3630 include numbers like 1, 2, 3, 5, 6, 10, 11, 15, 18, 22, 30, 33, 55, 66, 90, 110, 165, 198, 330, 363, 726, 1210, 1815, and 3630.
Negative factors of 3630: -1, -2, -3, -5, -6, -10, -11, -15, -18, -22, -30, -33, -55, -66, -90, -110, -165, -198, -330, -363, -726, -1210, -1815, and -3630.
Prime factors of 3630: 2, 3, 5, 11.
Prime factorization of 3630: 2 × 32 × 5 × 11.
The sum of factors of 3630: 12276
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 3630. Identifying the numbers which are multiplied to get the number 3630 is the multiplication method.
Step 1: Multiply 3630 by 1, 3630 × 1 = 3630.
Step 2: Check for other numbers that give 3630 after multiplying
2 × 1815 = 3630
3 × 1210 = 3630
5 × 726 = 3630
6 × 605 = 3630
10 × 363 = 3630
11 × 330 = 3630
15 × 242 = 3630
18 × 201 = 3630
22 × 165 = 3630
30 × 121 = 3630
33 × 110 = 3630
55 × 66 = 3630
Therefore, the positive factor pairs of 3630 are: (1, 3630), (2, 1815), (3, 1210), (5, 726), (6, 605), (10, 363), (11, 330), (15, 242), (18, 201), (22, 165), (30, 121), (33, 110), (55, 66). All these factor pairs result in 3630. For every positive factor, there is a negative factor.
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 3630 by 1, 3630 ÷ 1 = 3630.
Step 2: Continue dividing 3630 by the numbers until the remainder becomes 0.
3630 ÷ 1 = 3630
3630 ÷ 2 = 1815
3630 ÷ 3 = 1210
3630 ÷ 5 = 726
3630 ÷ 6 = 605
3630 ÷ 10 = 363
3630 ÷ 11 = 330
3630 ÷ 15 = 242
3630 ÷ 18 = 201
3630 ÷ 22 = 165
3630 ÷ 30 = 121
3630 ÷ 33 = 110
3630 ÷ 55 = 66
Therefore, the factors of 3630 are: 1, 2, 3, 5, 6, 10, 11, 15, 18, 22, 30, 33, 55, 66, 90, 110, 165, 198, 330, 363, 726, 1210, 1815, 3630.
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 3630 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3630 ÷ 2 = 1815
1815 ÷ 3 = 605
605 ÷ 5 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1
The prime factors of 3630 are 2, 3, 5, and 11.
The prime factorization of 3630 is: 2 × 32 × 5 × 11.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3630 is divided by 2 to get 1815.
Step 2: Now divide 1815 by 3 to get 605.
Step 3: Then divide 605 by 5 to get 121.
Step 4: Divide 121 by 11 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 3630 is: 2 × 32 × 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 3630: (1, 3630), (2, 1815), (3, 1210), (5, 726), (6, 605), (10, 363), (11, 330), (15, 242), (18, 201), (22, 165), (30, 121), (33, 110), and (55, 66).
Negative factor pairs of 3630: (-1, -3630), (-2, -1815), (-3, -1210), (-5, -726), (-6, -605), (-10, -363), (-11, -330), (-15, -242), (-18, -201), (-22, -165), (-30, -121), (-33, -110), and (-55, -66).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 33 students and 3630 pencils. How will they distribute them equally?
They will get 110 pencils each.
To distribute the pencils equally, we need to divide the total pencils by the number of students.
3630/33 = 110
A stadium's seating is arranged in 121 rows with a total of 3630 seats. How many seats are in each row?
30 seats.
To find the number of seats in each row, we use the formula,
Total seats = number of rows × seats per row
3630 = 121 × seats per row To find the number of seats per row, divide the total seats by the number of rows. 3630/121 = 30
A library has 726 books and wants to distribute them into 5 sections. How many books will be in each section?
Each section will have 145 books.
To find the books in each section, divide the total books by the number of sections.
726/5 = 145
There are 11 teams in a competition and 3630 points to be allocated equally among them. How many points does each team get?
Each team gets 330 points.
Dividing the points by the total teams, we will get the number of points each team receives.
3630/11 = 330
A company needs to distribute 1815 flyers across 6 locations. How many flyers will go to each location?
302 flyers.
Divide total flyers by the number of locations.
1815/6 = 302
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.