123 LearnersLast updated on May 26th, 2025
Factors of 3630
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.
What are the Factors of 3630?
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
How to Find Factors of 3630?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 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.
Finding Factors Using Division Method
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.
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 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.
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of 3630
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 3630, 1 and 3630 are also factors.
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 3630 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 3630/1.5 = 2420, 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 3630 are prime numbers.
For example, 2, 3, 5, and 11 are the prime factors of 3630, but it has other factors like 6, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3630 as 2 × 3^2 × 5 × 11 and missing all the key factors.
Factors of 3630 Examples
Problem 1
There are 33 students and 3630 pencils. How will they distribute them equally?
They will get 110 pencils each.
Explanation
To distribute the pencils equally, we need to divide the total pencils by the number of students.
3630/33 = 110
Problem 2
A stadium's seating is arranged in 121 rows with a total of 3630 seats. How many seats are in each row?
30 seats.
Explanation
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
Problem 3
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.
Explanation
To find the books in each section, divide the total books by the number of sections.
726/5 = 145
Problem 4
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.
Explanation
Dividing the points by the total teams, we will get the number of points each team receives.
3630/11 = 330
Problem 5
A company needs to distribute 1815 flyers across 6 locations. How many flyers will go to each location?
302 flyers.
Explanation
Divide total flyers by the number of locations.
1815/6 = 302
FAQs on Factors of 3630
1.What are the factors of 3630?
2.Mention the prime factors of 3630.
3.Is 3630 a multiple of 6?
4.Mention the factor pairs of 3630?
5.What is the square of 3630?
6.How can children in Thailand use numbers in everyday life to understand Factors of 3630?
7.What are some fun ways kids in Thailand can practice Factors of 3630 with numbers?
8.What role do numbers and Factors of 3630 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 3630 skills?
Important Glossaries for Factor of 3630
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, 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, and 3630.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 11 are prime factors of 3630.
- Prime factorization: The expression of a number as a product of its prime factors. For 3630, it is 2 × 32 × 5 × 11.
- 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 3630 are (1, 3630), (2, 1815), etc.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 3630 is a multiple of 6.
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About BrightChamps in Thailand
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.
