135 LearnersLast updated on May 26th, 2025
Factors of 1730
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 1730, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1730?
The numbers that divide 1730 evenly are known as factors of 1730.
A factor of 1730 is a number that divides the number without a remainder.
The factors of 1730 are 1, 2, 5, 10, 173, 346, 865, and 1730.
Negative factors of 1730: -1, -2, -5, -10, -173, -346, -865, and -1730.
Prime factors of 1730: 2, 5, and 173.
Prime factorization of 1730: 2 × 5 × 173.
The sum of factors of 1730: 1 + 2 + 5 + 10 + 173 + 346 + 865 + 1730 = 3132
How to Find Factors of 1730?
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 1730. Identifying the numbers that are multiplied to get the number 1730 is the multiplication method.
Step 1: Multiply 1730 by 1, 1730 × 1 = 1730.
Step 2: Check for other numbers that give 1730 after multiplying
2 × 865 = 1730
5 × 346 = 1730
10 × 173 = 1730
Therefore, the positive factor pairs of 1730 are: (1, 1730), (2, 865), (5, 346), (10, 173).
All these factor pairs result in 1730.
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 that result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1730 by 1, 1730 ÷ 1 = 1730.
Step 2: Continue dividing 1730 by the numbers until the remainder becomes 0.
1730 ÷ 1 = 1730
1730 ÷ 2 = 865
1730 ÷ 5 = 346
1730 ÷ 10 = 173
Therefore, the factors of 1730 are: 1, 2, 5, 10, 173, 346, 865, 1730.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 1730 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1730 ÷ 2 = 865
865 ÷ 5 = 173
173 ÷ 173 = 1
The prime factors of 1730 are 2, 5, and 173.
The prime factorization of 1730 is: 2 × 5 × 173.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1730 is divided by 2 to get 865.
Step 2: Now divide 865 by 5 to get 173.
Step 3: Divide 173 by 173 to get 1. Here, 173 is the smallest prime number, and it cannot be divided anymore.
So, the prime factorization of 1730 is: 2 × 5 × 173.
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 1730: (1, 1730), (2, 865), (5, 346), and (10, 173).
Negative factor pairs of 1730: (-1, -1730), (-2, -865), (-5, -346), and (-10, -173).
Common Mistakes and How to Avoid Them in Factors of 1730
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 1730, 1 and 1730 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 1730 consist of -1, -2, -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 as a factor, because 1730/1.5 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 1730 are prime numbers.
For example, 2, 5, and 173 are the prime factors of 1730, but it has other factors like 10, 346.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1730 as 2 × 5 × 173 and missing all the key factors.
Factors of 1730 Examples
Problem 1
A company has 1730 products and wants to pack them equally into 10 boxes. How many products will each box contain?
Each box will contain 173 products.
Explanation
To divide the products equally, we need to divide the total products by the number of boxes.
1730/10 = 173
Problem 2
A garden is rectangular, the length of the garden is 173 meters, and the total area is 1730 square meters. Find the width.
10 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1730 = 173 × width
To find the value of width, we need to shift 173 to the left side.
1730/173 = width
Width = 10.
Problem 3
There are 346 chairs and 5 rooms. How many chairs will be in each room?
Each room will have 69 chairs.
Explanation
To find the chairs in each room, divide the total chairs by the rooms.
346/5 = 69
Problem 4
In a class, there are 865 pencils and 173 students. How many pencils are there for each student?
There are 5 pencils for each student.
Explanation
Dividing the pencils with the total students, we will get the number of pencils for each student.
865/173 = 5
Problem 5
A library received 1730 new books and wants to distribute them equally on 2 shelves. How many books will go on each shelf?
Each of the shelves will have 865 books.
Explanation
Divide total books by shelves.
1730/2 = 865
FAQs on Factors of 1730
1.What are the factors of 1730?
2.Mention the prime factors of 1730.
3.Is 1730 a multiple of 173?
4.Mention the factor pairs of 1730?
5.What is the square of 1730?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1730?
7.What are some fun ways kids in Bahrain can practice Factors of 1730 with numbers?
8.What role do numbers and Factors of 1730 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1730 skills?
Important Glossaries for Factors of 1730
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1730 are 1, 2, 5, 10, 173, 346, 865, and 1730.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 173 are prime factors of 1730.
- 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 1730 are (1, 1730), (2, 865), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1730 is 2 × 5 × 173.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number. For example, using the multiplication method for 1730 results in factors such as (1, 1730) and (2, 865).
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About BrightChamps in Bahrain
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.
