Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To divide the products equally, we need to divide the total products by the number of boxes.
1730/10 = 173
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.
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.
There are 346 chairs and 5 rooms. How many chairs will be in each room?
Each room will have 69 chairs.
To find the chairs in each room, divide the total chairs by the rooms.
346/5 = 69
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.
Dividing the pencils with the total students, we will get the number of pencils for each student.
865/173 = 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.
Divide total books by shelves.
1730/2 = 865
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.
: She loves to read number jokes and games.