134 LearnersLast updated on May 26th, 2025
Factors of 1530
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 1530, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1530?
The numbers that divide 1530 evenly are known as factors of 1530. A factor of 1530 is a number that divides the number without remainder. The factors of 1530 are 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 153, 170, 255, 306, 510, 765, and 1530.
Negative factors of 1530: -1, -2, -3, -5, -6, -9, -10, -15, -17, -18, -30, -34, -45, -51, -85, -90, -153, -170, -255, -306, -510, -765, and -1530.
Prime factors of 1530: 2, 3, 5, and 17.
Prime factorization of 1530: 2 × 3 × 5 × 17.
The sum of factors of 1530: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 17 + 18 + 30 + 34 + 45 + 51 + 85 + 90 + 153 + 170 + 255 + 306 + 510 + 765 + 1530 = 4096
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
How to Find Factors of 1530?
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 1530. Identifying the numbers which are multiplied to get the number 1530 is the multiplication method.
Step 1: Multiply 1530 by 1, 1530 × 1 = 1530.
Step 2: Check for other numbers that give 1530 after multiplying
2 × 765 = 1530
3 × 510 = 1530
5 × 306 = 1530
6 × 255 = 1530
9 × 170 = 1530
10 × 153 = 1530
15 × 102 = 1530
17 × 90 = 1530
18 × 85 = 1530
30 × 51 = 1530
34 × 45 = 1530
Therefore, the positive factor pairs of 1530 are: (1, 1530), (2, 765), (3, 510), (5, 306), (6, 255), (9, 170), (10, 153), (15, 102), (17, 90), (18, 85), (30, 51), and (34, 45). 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 1530 by 1, 1530 ÷ 1 = 1530.
Step 2: Continue dividing 1530 by the numbers until the remainder becomes 0.
1530 ÷ 1 = 1530
1530 ÷ 2 = 765
1530 ÷ 3 = 510
1530 ÷ 5 = 306
1530 ÷ 6 = 255
1530 ÷ 9 = 170
1530 ÷ 10 = 153
1530 ÷ 15 = 102
1530 ÷ 17 = 90
1530 ÷ 18 = 85
1530 ÷ 30 = 51
1530 ÷ 34 = 45
Therefore, the factors of 1530 are: 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 153, 170, 255, 306, 510, 765, and 1530.
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 1530 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1530 ÷ 2 = 765
765 ÷ 3 = 255
255 ÷ 3 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
The prime factors of 1530 are 2, 3, 5, and 17. The prime factorization of 1530 is: 2 × 3 × 5 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1530 is divided by 2 to get 765.
Step 2: Now divide 765 by 3 to get 255.
Step 3: Then divide 255 by 3 to get 85.
Step 4: Divide 85 by 5 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1530 is: 2 × 3 × 5 × 17.
:
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 1530: (1, 1530), (2, 765), (3, 510), (5, 306), (6, 255), (9, 170), (10, 153), (15, 102), (17, 90), (18, 85), (30, 51), and (34, 45).
- Negative factor pairs of 1530: (-1, -1530), (-2, -765), (-3, -510), (-5, -306), (-6, -255), (-9, -170), (-10, -153), (-15, -102), (-17, -90), (-18, -85), (-30, -51), and (-34, -45).
Common Mistakes and How to Avoid Them in Factors of 1530
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 1530, 1 and 1530 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 1530 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, because 1530/1.5 does not result in 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 1530 are prime numbers. While 2, 3, 5, and 17 are the prime factors of 1530, it has other factors like 6, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors. For example, not breaking 1530 as 2 × 3 × 5 × 17 and missing key factors.
Level Up with a Math Certification!
2X Faster Learning (Grades 1-12)
Factors of 1530 Examples
Problem 1
There are 51 students and 1530 books. How will they distribute them equally among themselves?
They will get 30 books each.
Explanation
To distribute the books equally, divide the total number of books by the number of students.
1530/51 = 30
Problem 2
A rectangular garden has a length of 90 meters and a total area of 1530 square meters. What is the width?
17 meters.
Explanation
To find the width of the garden, use the formula,
Area = length × width
1530 = 90 × width
To find the width, divide 1530 by 90.
1530/90 = width
Width = 17
Problem 3
A baker has 170 cookies and wants to pack them equally into boxes containing 9 cookies each. How many boxes will he need?
19 boxes.
Explanation
To find how many boxes are needed, divide the total cookies by the number of cookies per box.
170/9 = 18.888... which rounds up to 19 (as partial boxes aren't practical).
Problem 4
In a competition, there are 1530 participants and 17 teams. How many participants are there in each team?
There are 90 participants in each team.
Explanation
Divide the number of participants by the number of teams to find the number of participants in each team.
1530/17 = 90
Problem 5
1530 bottles need to be distributed equally into 10 crates. How many bottles will go in each crate?
Each crate will have 153 bottles.
Explanation
Divide the total number of bottles by the number of crates.
1530/10 = 153
Turn your child into a math star!
#1 Math Hack Schools Won't Teach!
FAQs on Factors of 1530
1.What are the factors of 1530?
2.Mention the prime factors of 1530.
3.Is 1530 a multiple of 5?
4.Mention the factor pairs of 1530?
5.What is the square of 1530?
6.How can children in India use numbers in everyday life to understand Factors of 1530?
7.What are some fun ways kids in India can practice Factors of 1530 with numbers?
8.What role do numbers and Factors of 1530 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 1530 skills?
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
Important Glossaries for Factors of 1530
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1530 are 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 153, 170, 255, 306, 510, 765, and 1530.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 17 are prime factors of 1530.
- 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 1530 are (1, 1530), (2, 765), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 1530 is 2 × 3 × 5 × 17.
- Multiple: A number that can be divided by another number without a remainder. For example, 1530 is a multiple of 5.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 1530
About BrightChamps in India
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.
