120 LearnersLast updated on May 26th, 2025
Factors of 3645
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 3645, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 3645?
The numbers that divide 3645 evenly are known as factors of 3645.
A factor of 3645 is a number that divides the number without remainder.
The factors of 3645 include numbers such as 1, 3, 5, 9, 15, 27, 45, 81, 1215, and 3645.
Negative factors of 3645: -1, -3, -5, -9, -15, -27, -45, -81, -1215, and -3645.
Prime factors of 3645: 3 and 5.
Prime factorization of 3645: 34 × 5 × 81.
The sum of factors of 3645: 1 + 3 + 5 + 9 + 15 + 27 + 45 + 81 + 1215 + 3645 = 5046
How to Find Factors of 3645?
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 3645. Identifying the numbers which are multiplied to get the number 3645 is the multiplication method.
Step 1: Multiply 3645 by 1, 3645 × 1 = 3645.
Step 2: Check for other numbers that give 3645 after multiplying
3 × 1215 = 3645
5 × 729 = 3645
9 × 405 = 3645
15 × 243 = 3645
27 × 135 = 3645
45 × 81 = 3645
Therefore, the positive factor pairs of 3645 are: (1, 3645), (3, 1215), (5, 729), (9, 405), (15, 243), (27, 135), and (45, 81). 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 3645 by 1, 3645 ÷ 1 = 3645.
Step 2: Continue dividing 3645 by the numbers until the remainder becomes 0.
3645 ÷ 1 = 3645
3645 ÷ 3 = 1215
3645 ÷ 5 = 729
3645 ÷ 9 = 405
3645 ÷ 15 = 243
3645 ÷ 27 = 135
3645 ÷ 45 = 81
Therefore, the factors of 3645 are: 1, 3, 5, 9, 15, 27, 45, 81, 1215, and 3645.
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 3645 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3645 ÷ 3 = 1215
1215 ÷ 3 = 405
405 ÷ 3 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of 3645 are 3 and 5.
The prime factorization of 3645 is: 35 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3645 is divided by 3 to get 1215.
Step 2: Now divide 1215 by 3 to get 405.
Step 3: Then divide 405 by 3 to get 135.
Step 4: Divide 135 by 3 to get 45.
Step 5: Divide 45 by 3 to get 15.
Step 6: Divide 15 by 3 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 3645 is: 35 × 5.
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 3645: (1, 3645), (3, 1215), (5, 729), (9, 405), (15, 243), (27, 135), (45, 81).
Negative factor pairs of 3645: (-1, -3645), (-3, -1215), (-5, -729), (-9, -405), (-15, -243), (-27, -135), (-45, -81).
Common Mistakes and How to Avoid Them in Factors of 3645
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 3645, 1 and 3645 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 3645 include -1, -3, -5, 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 is a factor because 3645/1.5 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 3645 are prime numbers.
For example, 3 and 5 are the prime factors of 3645, but it has other factors like 9, 45, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3645 as 35 × 5 and missing all the key factors.
Factors of 3645 Examples
Problem 1
There are 9 friends and 3645 chocolates. How will they divide them equally?
They will get 405 chocolates each.
Explanation
To divide the chocolates equally, we need to divide the total chocolates by the number of friends.
3645/9 = 405
Problem 2
A field is rectangular, the length of the field is 81 meters, and the total area is 3645 square meters. Find the width.
45 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
3645 = 81 × width
To find the value of width, we need to shift 81 to the left side.
3645/81 = width
Width = 45.
Problem 3
There are 27 bags and 3645 marbles. How many marbles will be in each bag?
Each bag will have 135 marbles.
Explanation
To find the marbles in each bag, divide the total marbles by the bags.
3645/27 = 135
Problem 4
In a class, there are 3645 students, and 405 groups. How many students are there in each group?
There are 9 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
3645/405 = 9
Problem 5
3645 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 729 books.
Explanation
Divide total books by shelves.
3645/5 = 729
FAQs on Factors of 3645
1.What are the factors of 3645?
2.Mention the prime factors of 3645.
3.Is 3645 a multiple of 9?
4.Mention the factor pairs of 3645?
5.What is the square of 3645?
6.How can children in Australia use numbers in everyday life to understand Factors of 3645?
7.What are some fun ways kids in Australia can practice Factors of 3645 with numbers?
8.What role do numbers and Factors of 3645 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 3645 skills?
Important Glossaries for Factor of 3645
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3645 are 1, 3, 5, 9, 15, 27, 45, 81, 1215, and 3645.
- Prime factors: The factors which are prime numbers. For example, 3 and 5 are prime factors of 3645.
- 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 3645 are (1, 3645), (3, 1215), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 3645 is 35 × 5.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to give the original number, such as finding factor pairs of 3645.
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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
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