119 LearnersLast updated on May 26th, 2025
Factors of 1635
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 1635, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1635?
The numbers that divide 1635 evenly are known as factors of 1635.
A factor of 1635 is a number that divides the number without a remainder.
The factors of 1635 are 1, 3, 5, 15, 109, 327, 545, and 1635.
Negative factors of 1635: -1, -3, -5, -15, -109, -327, -545, and -1635.
Prime factors of 1635: 3, 5, and 109.
Prime factorization of 1635: 3 × 5 × 109.
The sum of factors of 1635: 1 + 3 + 5 + 15 + 109 + 327 + 545 + 1635 = 2640
How to Find Factors of 1635?
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 1635. Identifying the numbers which are multiplied to get the number 1635 is the multiplication method.
Step 1: Multiply 1635 by 1, 1635 × 1 = 1635.
Step 2: Check for other numbers that give 1635 after multiplying
3 × 545 = 1635
5 × 327 = 1635
15 × 109 = 1635
Therefore, the positive factor pairs of 1635 are: (1, 1635), (3, 545), (5, 327), and (15, 109). All these factor pairs result in 1635.
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 as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1635 by 1, 1635 ÷ 1 = 1635.
Step 2: Continue dividing 1635 by the numbers until the remainder becomes 0.
1635 ÷ 1 = 1635
1635 ÷ 3 = 545
1635 ÷ 5 = 327
1635 ÷ 15 = 109
Therefore, the factors of 1635 are: 1, 3, 5, 15, 109, 327, 545, 1635.
Prime Factors and Prime Factorization
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using a factor tree
Using Prime Factorization: In this process, prime factors of 1635 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1635 ÷ 3 = 545
545 ÷ 5 = 109
109 ÷ 109 = 1
The prime factors of 1635 are 3, 5, and 109.
The prime factorization of 1635 is: 3 × 5 × 109.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1635 is divided by 3 to get 545.
Step 2: Now divide 545 by 5 to get 109.
Step 3: 109 is a prime number, so it cannot be divided anymore. So, the prime factorization of 1635 is: 3 × 5 × 109.
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 1635: (1, 1635), (3, 545), (5, 327), and (15, 109).
Negative factor pairs of 1635: (-1, -1635), (-3, -545), (-5, -327), and (-15, -109).
Common Mistakes and How to Avoid Them in Factors of 1635
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 1635, 1 and 1635 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 1635 include -1, -3, -5, 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, because 1635/1.5 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 1635 are prime numbers. For example, 3, 5, and 109 are the prime factors of 1635, but it has other factors like 15, 545.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1635 as 3 × 5 × 109 and missing key factors.
Factors of 1635 Examples
Problem 1
A farmer has 1635 apples to be packed equally in 3 boxes. How many apples will each box contain?
Each box will contain 545 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of boxes.
1635/3 = 545
Problem 2
A conference hall has a seating capacity of 1635, and there are 5 rows. How many seats are there in each row?
There are 327 seats in each row.
Explanation
To find the number of seats in each row, we use the formula, Total seats = number of rows × seats per row
1635 = 5 × seats per row
To find the number of seats per row, divide: 1635/5 = 327
Problem 3
A library has 1635 books, and they need to be distributed equally across 15 shelves. How many books will each shelf contain?
Each shelf will contain 109 books.
Explanation
To find the books on each shelf, divide the total books by the number of shelves.
1635/15 = 109
Problem 4
A total of 1635 people are attending a concert, and they are divided into 109 groups. How many people are in each group?
There are 15 people in each group.
Explanation
Dividing the people by the total groups, we will get the number of people in each group.
1635/109 = 15
Problem 5
1635 chairs need to be arranged in 5 sections. How many chairs will go in each section?
Each section will have 327 chairs.
Explanation
Divide the total chairs by the sections.
1635/5 = 327
FAQs on Factors of 1635
1.What are the factors of 1635?
2.Mention the prime factors of 1635.
3.Is 1635 a multiple of 3?
4.Mention the factor pairs of 1635?
5.What is the square of 1635?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1635?
7.What are some fun ways kids in Qatar can practice Factors of 1635 with numbers?
8.What role do numbers and Factors of 1635 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1635 skills?
Important Glossaries for Factor of 1635
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1635 are 1, 3, 5, 15, 109, 327, 545, and 1635.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 109 are prime factors of 1635.
- 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 1635 are (1, 1635), (3, 545), etc.
- Prime factorization: The process of breaking a number down into its prime factors. For instance, the prime factorization of 1635 is 3 × 5 × 109.
- Negative factors: Whole numbers that divide the given number resulting in a negative quotient. For 1635, negative factors include -1, -3, -5, etc.
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About BrightChamps in Qatar
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.
