131 LearnersLast updated on May 26th, 2025
Factors of 1745
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 1745, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1745?
The numbers that divide 1745 evenly are known as factors of 1745.
A factor of 1745 is a number that divides the number without remainder.
The factors of 1745 are 1, 5, 349, and 1745.
Negative factors of 1745: -1, -5, -349, and -1745.
Prime factors of 1745: 5 and 349.
Prime factorization of 1745: 5 × 349.
The sum of factors of 1745: 1 + 5 + 349 + 1745 = 2100
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How to Find Factors of 1745?
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 1745. Identifying the numbers which are multiplied to get the number 1745 is the multiplication method.
Step 1: Multiply 1745 by 1, 1745 × 1 = 1745.
Step 2: Check for other numbers that give 1745 after multiplying 5 × 349 = 1745
Therefore, the positive factor pairs of 1745 are: (1, 1745), (5, 349).
All these factor pairs result in 1745.
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 1745 by 1, 1745 ÷ 1 = 1745.
Step 2: Continue dividing 1745 by the numbers until the remainder becomes 0.
1745 ÷ 1 = 1745
1745 ÷ 5 = 349
Therefore, the factors of 1745 are: 1, 5, 349, 1745.
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 1745 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1745 ÷ 5 = 349
349 ÷ 349 = 1
The prime factors of 1745 are 5 and 349.
The prime factorization of 1745 is: 5 × 349.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1745 is divided by 5 to get 349.
Step 2: Divide 349 by 349 to get 1. Here, 349 is a prime number and cannot be divided anymore.
So, the prime factorization of 1745 is: 5 × 349.
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 1745: (1, 1745), (5, 349).
Negative factor pairs of 1745: (-1, -1745), (-5, -349).
Common Mistakes and How to Avoid Them in Factors of 1745
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 1745, 1 and 1745 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 1745 consist of -1, -5, -349, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.75 as a factor, because 1745/1.75 = 997.1428, 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 1745 are prime numbers.
For example, 5 and 349 are the prime factors of 1745, but it has other factors like 1, 1745.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1745 as 5 × 349 and missing all the key factors.
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Factors of 1745 Examples
Problem 1
A farmer has 5 plots of land and 1745 trees. How many trees will each plot receive if distributed equally?
Each plot will receive 349 trees.
Explanation
To distribute the trees equally, we need to divide the total number of trees by the number of plots.
1745/5 = 349
Problem 2
A rectangular garden has a length of 349 meters and a total area of 1745 square meters. Find the width.
5 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1745 = 349 × width
To find the value of width, we need to shift 349 to the left side.
1745/349 = width
Width = 5.
Problem 3
A warehouse has 1745 boxes and needs to be organized into 5 sections. How many boxes will be in each section?
Each section will have 349 boxes.
Explanation
To find the number of boxes in each section, divide the total number of boxes by the number of sections.
1745/5 = 349
Problem 4
A company has 1745 units of product and needs to pack them into boxes of 349 units each. How many boxes are needed?
5 boxes are needed.
Explanation
Dividing the total units by the units per box, we will get the number of boxes.
1745/349 = 5
Problem 5
A library has 5 shelves and 1745 books. How many books will go on each shelf?
Each shelf will have 349 books.
Explanation
Divide the total number of books by the number of shelves.
1745/5 = 349
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FAQs on Factors of 1745
1.What are the factors of 1745?
2.Mention the prime factors of 1745.
3.Is 1745 a multiple of 5?
4.Mention the factor pairs of 1745?
5.What is the square of 1745?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1745?
7.What are some fun ways kids in Bahrain can practice Factors of 1745 with numbers?
8.What role do numbers and Factors of 1745 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1745 skills?
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Important Glossaries for Factor of 1745
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1745 are 1, 5, 349, and 1745.
- Prime factors: The factors which are prime numbers. For example, 5 and 349 are prime factors of 1745.
- 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 1745 are (1, 1745) and (5, 349).
- Negative factors: Factors that are negative numbers, such as -1, -5, -349, and -1745 for 1745.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, 1745 can be expressed as 5 × 349.
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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.
