100 LearnersLast updated on May 26th, 2025
Factors of 1740
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 1740, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1740?
The numbers that divide 1740 evenly are known as factors of 1740.
A factor of 1740 is a number that divides the number without a remainder.
The factors of 1740 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116, 145, 174, 290, 348, 435, 580, 870, and 1740.
Negative factors of 1740: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -29, -30, -58, -60, -87, -116, -145, -174, -290, -348, -435, -580, -870, and -1740.
Prime factors of 1740: 2, 3, 5, and 29.
Prime factorization of 1740: 22 × 3 × 5 × 29.
The sum of factors of 1740: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 29 + 30 + 58 + 60 + 87 + 116 + 145 + 174 + 290 + 348 + 435 + 580 + 870 + 1740 = 5712
How to Find Factors of 1740?
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 1740. Identifying the numbers which are multiplied to get the number 1740 is the multiplication method.
Step 1: Multiply 1740 by 1, 1740 × 1 = 1740.
Step 2: Check for other numbers that give 1740 after multiplying
2 × 870 = 1740
3 × 580 = 1740
4 × 435 = 1740
5 × 348 = 1740
6 × 290 = 1740
10 × 174 = 1740
12 × 145 = 1740
15 × 116 = 1740
20 × 87 = 1740
29 × 60 = 1740
30 × 58 = 1740
Therefore, the positive factor pairs of 1740 are: (1, 1740), (2, 870), (3, 580), (4, 435), (5, 348), (6, 290), (10, 174), (12, 145), (15, 116), (20, 87), (29, 60), (30, 58).
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 the simple division method
Step 1: Divide 1740 by 1, 1740 ÷ 1 = 1740.
Step 2: Continue dividing 1740 by the numbers until the remainder becomes 0.
1740 ÷ 1 = 1740
1740 ÷ 2 = 870
1740 ÷ 3 = 580
1740 ÷ 4 = 435
1740 ÷ 5 = 348
1740 ÷ 6 = 290
1740 ÷ 10 = 174
1740 ÷ 12 = 145
1740 ÷ 15 = 116
1740 ÷ 20 = 87
1740 ÷ 29 = 60
1740 ÷ 30 = 58
Therefore, the factors of 1740 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116, 145, 174, 290, 348, 435, 580, 870, and 1740.
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 1740 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1740 ÷ 2 = 870
870 ÷ 2 = 435
435 ÷ 3 = 145
145 ÷ 5 = 29
29 ÷ 29 = 1
The prime factors of 1740 are 2, 3, 5, and 29.
The prime factorization of 1740 is: 22 × 3 × 5 × 29.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1740 is divided by 2 to get 870.
Step 2: Now divide 870 by 2 to get 435.
Step 3: Then divide 435 by 3 to get 145.
Step 4: Divide 145 by 5 to get 29. Here, 29 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1740 is: 22 × 3 × 5 × 29.
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 1740: (1, 1740), (2, 870), (3, 580), (4, 435), (5, 348), (6, 290), (10, 174), (12, 145), (15, 116), (20, 87), (29, 60), (30, 58).
Negative factor pairs of 1740: (-1, -1740), (-2, -870), (-3, -580), (-4, -435), (-5, -348), (-6, -290), (-10, -174), (-12, -145), (-15, -116), (-20, -87), (-29, -60), (-30, -58).
Common Mistakes and How to Avoid Them in Factors of 1740
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 1740, 1 and 1740 are also factors.
Factors of 1740 Examples
Problem 1
There are 87 students and 1740 pencils. How will they divide it equally?
They will get 20 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils with the number of students.
1740/87 = 20
Problem 2
A garden is rectangular, the length of the garden is 58 meters and the total area is 1740 square meters. Find the width?
30 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1740 = 58 × width
To find the value of width, we need to shift 58 to the left side.
1740/58 = width
Width = 30.
Problem 3
There are 29 tables and 1740 chairs. How many chairs will be at each table?
Each table will have 60 chairs.
Explanation
To find the chairs at each table, divide the total chairs with tables.
1740/29 = 60
Problem 4
In a stadium, there are 1740 seats and 145 sections. How many seats are there in each section?
There are 12 seats in each section.
Explanation
Dividing the seats with the total sections, we will get the number of seats in each section.
1740/145 = 12
Problem 5
1740 books need to be arranged in 58 shelves. How many books will go on each shelf?
Each of the shelves has 30 books.
Explanation
Divide total books with shelves.
1740/58 = 30
FAQs on Factors of 1740
1.What are the factors of 1740?
2.Mention the prime factors of 1740.
3.Is 1740 a multiple of 29?
4.Mention the factor pairs of 1740?
5.What is the square of 1740?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1740?
7.What are some fun ways kids in Bahrain can practice Factors of 1740 with numbers?
8.What role do numbers and Factors of 1740 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1740 skills?
Important Glossaries for Factor of 1740
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1740 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116, 145, 174, 290, 348, 435, 580, 870, and 1740.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 29 are prime factors of 1740.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1740 is 22 × 3 × 5 × 29.
- 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 1740 are (1, 1740), (2, 870), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method for 1740 involves pairs like 2 × 870.
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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.
Fun Fact
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