117 LearnersLast updated on May 26th, 2025
Factors of 3600
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 3600, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 3600?
The numbers that divide 3600 evenly are known as factors of 3600.
A factor of 3600 is a number that divides the number without a remainder.
The factors of 3600 include 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, and 3600.
Negative factors of 3600: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -25, -30, -36, -40, -45, -48, -50, -60, -72, -75, -80, -90, -100, -120, -144, -150, -180, -200, -225, -240, -300, -360, -400, -450, -600, -720, -900, -1200, -1800, and -3600.
Prime factors of 3600: 2, 3, and 5.
Prime factorization of 3600: 24 × 32 × 52.
The sum of factors of 3600: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 30 + 36 + 40 + 45 + 48 + 50 + 60 + 72 + 75 + 80 + 90 + 100 + 120 + 144 + 150 + 180 + 200 + 225 + 240 + 300 + 360 + 400 + 450 + 600 + 720 + 900 + 1200 + 1800 + 3600 = 12483
How to Find Factors of 3600?
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 3600. Identifying the numbers which are multiplied to get the number 3600 is the multiplication method.
Step 1: Multiply 3600 by 1, 3600 × 1 = 3600.
Step 2: Check for other numbers that give 3600 after multiplying
2 × 1800 = 3600
3 × 1200 = 3600
4 × 900 = 3600
5 × 720 = 3600
6 × 600 = 3600
8 × 450 = 3600
9 × 400 = 3600
10 × 360 = 3600
12 × 300 = 3600
15 × 240 = 3600
16 × 225 = 3600
18 × 200 = 3600
20 × 180 = 3600
24 × 150 = 3600
25 × 144 = 3600
30 × 120 = 3600
36 × 100 = 3600
40 × 90 = 3600
45 × 80 = 3600
48 × 75 = 3600
50 × 72 = 3600
60 × 60 = 3600
Therefore, the positive factor pairs of 3600 include: (1, 3600), (2, 1800), (3, 1200), (4, 900), (5, 720), (6, 600), (8, 450), (9, 400), (10, 360), (12, 300), (15, 240), (16, 225), (18, 200), (20, 180), (24, 150), (25, 144), (30, 120), (36, 100), (40, 90), (45, 80), (48, 75), and (50, 72). 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 3600 by 1, 3600 ÷ 1 = 3600.
Step 2: Continue dividing 3600 by the numbers until the remainder becomes 0.
3600 ÷ 1 = 3600
3600 ÷ 2 = 1800
3600 ÷ 3 = 1200
3600 ÷ 4 = 900
3600 ÷ 5 = 720
3600 ÷ 6 = 600
3600 ÷ 8 = 450
3600 ÷ 9 = 400
3600 ÷ 10 = 360
3600 ÷ 12 = 300
3600 ÷ 15 = 240
3600 ÷ 16 = 225
3600 ÷ 18 = 200
3600 ÷ 20 = 180
3600 ÷ 24 = 150
3600 ÷ 25 = 144
3600 ÷ 30 = 120
3600 ÷ 36 = 100
3600 ÷ 40 = 90
3600 ÷ 45 = 80
3600 ÷ 48 = 75
3600 ÷ 50 = 72
3600 ÷ 60 = 60
Therefore, the factors of 3600 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, and 3600.
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 3600 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3600 ÷ 2 = 1800
1800 ÷ 2 = 900
900 ÷ 2 = 450
450 ÷ 3 = 150
150 ÷ 3 = 50
50 ÷ 5 = 10
10 ÷ 5 = 2
The prime factors of 3600 are 2, 3, and 5.
The prime factorization of 3600 is: 24 × 32 × 52.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 3600 is divided by 2 to get 1800.
Step 2: Now divide 1800 by 2 to get 900.
Step 3: Then divide 900 by 2 to get 450.
Step 4: Divide 450 by 3 to get 150.
Step 5: Divide 150 by 3 to get 50.
Step 6: Divide 50 by 5 to get 10.
Step 7: Divide 10 by 5 to get 2. Here, 2 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 3600 is: 24 × 32 × 52.
Factor Pairs: Two numbers that are multiplied to give a specific number are called as factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 3600: (1, 3600), (2, 1800), (3, 1200), (4, 900), (5, 720), (6, 600), (8, 450), (9, 400), (10, 360), (12, 300), (15, 240), (16, 225), (18, 200), (20, 180), (24, 150), (25, 144), (30, 120), (36, 100), (40, 90), (45, 80), (48, 75), and (50, 72).
Negative factor pairs of 3600: (-1, -3600), (-2, -1800), (-3, -1200), (-4, -900), (-5, -720), (-6, -600), (-8, -450), (-9, -400), (-10, -360), (-12, -300), (-15, -240), (-16, -225), (-18, -200), (-20, -180), (-24, -150), (-25, -144), (-30, -120), (-36, -100), (-40, -90), (-45, -80), (-48, -75), and (-50, -72).
Common Mistakes and How to Avoid Them in Factors of 3600
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 3600, 1 and 3600 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 3600 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor is incorrect because 3600/1.5 = 2400, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not just primes.
For example, thinking all the factors of 3600 are prime numbers is incorrect. While 2, 3, and 5 are the prime factors of 3600, it also has other factors like 4, 9, and 10.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking 3600 as 2^4 × 3^2 × 5^2 and missing key factors.
Factors of 3600 Examples
Problem 1
There are 36 people and 3600 apples. How will they divide them equally?
They will get 100 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of people.
3600/36 = 100
Problem 2
A garden is rectangular, the length of the garden is 60 meters, and the total area is 3600 square meters. Find the width.
60 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
3600 = 60 × width
To find the value of width, we need to shift 60 to the left side.
3600/60 = width
Width = 60.
Problem 3
There are 24 containers and 3600 oranges. How many oranges will be in each container?
Each container will have 150 oranges.
Explanation
To find the oranges in each container, divide the total oranges by the containers.
3600/24 = 150
Problem 4
In a conference, there are 3600 participants and 45 groups. How many participants are there in each group?
There are 80 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group.
3600/45 = 80
Problem 5
3600 papers need to be arranged in 12 stacks. How many papers will go in each stack?
Each stack has 300 papers.
Explanation
Divide the total papers by the stacks.
3600/12 = 300
FAQs on Factors of 3600
1.What are the factors of 3600?
2.Mention the prime factors of 3600.
3.Is 3600 a multiple of 4?
4.Mention the factor pairs of 3600?
5.What is the square of 3600?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 3600?
7.What are some fun ways kids in United Kingdom can practice Factors of 3600 with numbers?
8.What role do numbers and Factors of 3600 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 3600 skills?
Important Glossaries for Factors of 3600
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3600 are 1, 2, 3, 4, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 3600.
- 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 3600 are (1, 3600), (2, 1800), etc.
- Prime factorization: The process of breaking down a number into the product of its prime factors. For example, the prime factorization of 3600 is 24 × 32 × 52.
- Multiples: Numbers that can be divided by another number without a remainder. For example, 3600 is a multiple of 4.
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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.
