118 LearnersLast updated on May 26th, 2025
Factors of 1035
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 1035, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1035?
The numbers that divide 1035 evenly are known as factors of 1035.
A factor of 1035 is a number that divides the number without remainder.
The factors of 1035 are 1, 3, 5, 15, 23, 69, 115, 345, and 1035.
Negative factors of 1035: -1, -3, -5, -15, -23, -69, -115, -345, and -1035.
Prime factors of 1035: 3, 5, and 23.
Prime factorization of 1035: 3 × 5 × 23.
The sum of factors of 1035: 1 + 3 + 5 + 15 + 23 + 69 + 115 + 345 + 1035 = 1611
How to Find Factors of 1035?
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 1035. Identifying the numbers which are multiplied to get the number 1035 is the multiplication method.
Step 1: Multiply 1035 by 1, 1035 × 1 = 1035.
Step 2: Check for other numbers that give 1035 after multiplying:
3 × 345 = 1035
5 × 207 = 1035
15 × 69 = 1035
23 × 45 = 1035
Therefore, the positive factor pairs of 1035 are: (1, 1035), (3, 345), (5, 207), (15, 69), (23, 45). All these factor pairs result in 1035. For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number 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 1035 by 1, 1035 ÷ 1 = 1035.
Step 2: Continue dividing 1035 by the numbers until the remainder becomes 0.
1035 ÷ 1 = 1035
1035 ÷ 3 = 345
1035 ÷ 5 = 207
1035 ÷ 15 = 69
1035 ÷ 23 = 45
Therefore, the factors of 1035 are: 1, 3, 5, 15, 23, 69, 115, 345, 1035.
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 1035 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1035 ÷ 3 = 345
345 ÷ 3 = 115
115 ÷ 5 = 23
23 ÷ 23 = 1
The prime factors of 1035 are 3, 5, and 23.
The prime factorization of 1035 is: 3 × 5 × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 1035 is divided by 3 to get 345.
Step 2: Now divide 345 by 3 to get 115.
Step 3: Then divide 115 by 5 to get 23. Here, 23 is the smallest prime number, which cannot be divided anymore. So, the prime factorization of 1035 is: 3 × 5 × 23.
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 1035: (1, 1035), (3, 345), (5, 207), (15, 69), and (23, 45).
Negative factor pairs of 1035: (-1, -1035), (-3, -345), (-5, -207), (-15, -69), and (-23, -45).
Common Mistakes and How to Avoid Them in Factors of 1035
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 1035, 1 and 1035 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 1035 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 2.5 as a factor, because 1035/2.5 = 414, 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 1035 are prime numbers.
For example, 3, 5, and 23 are the prime factors of 1035, but it has other factors like 15, 69.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1035 as 3 × 5 × 23 and missing all the key factors.
Factors of 1035 Examples
Problem 1
There are 15 people and 1035 candies. How will they divide it equally?
They will get 69 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of people.
1035/15 = 69
Problem 2
A rectangular painting has a length of 23 inches and a total area of 1035 square inches. Find the width.
45 inches.
Explanation
To find the width of the painting, we use the formula,
Area = length × width
1035 = 23 × width
To find the value of width, we need to shift 23 to the left side.
1035/23 = width
Width = 45.
Problem 3
There are 69 bags and 1035 apples. How many apples will be in each bag?
Each bag will have 15 apples.
Explanation
To find the apples in each bag, divide the total apples by the bags.
1035/69 = 15
Problem 4
In a theater, there are 345 seats and 5 sections. How many seats are there in each section?
There are 69 seats in each section.
Explanation
Dividing the seats by the total sections, we will get the number of seats in each section.
345/5 = 69
Problem 5
1035 books need to be arranged in 23 shelves. How many books will go on each shelf?
Each of the shelves has 45 books.
Explanation
Divide the total books by shelves.
1035/23 = 45
FAQs on Factors of 1035
1.What are the factors of 1035?
2.Mention the prime factors of 1035.
3.Is 1035 a multiple of 5?
4.Mention the factor pairs of 1035?
5.What is the square of 1035?
6.How can children in Indonesia use numbers in everyday life to understand Factors of 1035?
7.What are some fun ways kids in Indonesia can practice Factors of 1035 with numbers?
8.What role do numbers and Factors of 1035 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Factors of 1035 skills?
Important Glossaries for Factor of 1035
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1035 are 1, 3, 5, 15, 23, 69, 115, 345, and 1035.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 23 are prime factors of 1035.
- 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 1035 are (1, 1035), (3, 345), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1035 is 3 × 5 × 23.
- Negative factors: These are the negative counterparts of the positive factors. For example, the negative factors of 1035 include -1, -3, -5, etc.
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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.
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