130 LearnersLast updated on May 26th, 2025
Factors of 1743
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 1743, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1743?
The numbers that divide 1743 evenly are known as factors of 1743.
A factor of 1743 is a number that divides the number without a remainder.
The factors of 1743 are 1, 3, 7, 9, 21, 29, 63, 87, 203, 261, 581, and 1743.
Negative factors of 1743: -1, -3, -7, -9, -21, -29, -63, -87, -203, -261, -581, and -1743.
Prime factors of 1743: 3, 7, and 29.
Prime factorization of 1743: 3 × 7 × 83.
The sum of factors of 1743: 1 + 3 + 7 + 9 + 21 + 29 + 63 + 87 + 203 + 261 + 581 + 1743 = 3008
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How to Find Factors of 1743?
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 1743. Identifying the numbers which are multiplied to get the number 1743 is the multiplication method.
Step 1: Multiply 1743 by 1, 1743 × 1 = 1743.
Step 2: Check for other numbers that give 1743 after multiplying
3 × 581 = 1743
7 × 249 = 1743
9 × 193 = 1743
21 × 83 = 1743
29 × 61 = 1743
Therefore, the positive factor pairs of 1743 are: (1, 1743), (3, 581), (7, 249), (9, 193), (21, 83), and (29, 61).
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1743 by 1, 1743 ÷ 1 = 1743.
Step 2: Continue dividing 1743 by the numbers until the remainder becomes 0.
1743 ÷ 1 = 1743
1743 ÷ 3 = 581
1743 ÷ 7 = 249
1743 ÷ 9 = 193
1743 ÷ 21 = 83
Therefore, the factors of 1743 are: 1, 3, 7, 9, 21, 29, 63, 87, 203, 261, 581, 1743.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 1743 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1743 ÷ 3 = 581
581 ÷ 7 = 83
83 ÷ 29 = 1
The prime factors of 1743 are 3, 7, and 29.
The prime factorization of 1743 is: 3 × 7 × 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, 1743 is divided by 3 to get 581.
Step 2: Now divide 581 by 7 to get 83.
Step 3: Divide 83 by 29 to get 1.
So, the prime factorization of 1743 is: 3 × 7 × 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 1743: (1, 1743), (3, 581), (7, 249), (9, 193), (21, 83), and (29, 61).
Negative factor pairs of 1743: (-1, -1743), (-3, -581), (-7, -249), (-9, -193), (-21, -83), and (-29, -61).
Common Mistakes and How to Avoid Them in Factors of 1743
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1743, 1 and 1743 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 1743 consist of -1, -3, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor is incorrect because 1743/1.5 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 1743 are prime numbers. While 3, 7, and 29 are the prime factors of 1743, it has other factors like 9, 21.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing incorrect factors.
For example, not breaking 1743 into 3 × 7 × 29 and missing all the key factors.
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Factors of 1743 Examples
Problem 1
There are 3 students and 1743 pages. How will they divide it equally?
They will get 581 pages each.
Explanation
To divide the pages equally, we need to divide the total pages by the number of students.
1743/3 = 581
Problem 2
A rectangular garden has a length of 29 meters and a total area of 1743 square meters. Find the width?
The width is 61 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1743 = 29 × width
To find the value of width, we need to shift 29 to the left side.
1743/29 = width
Width = 61.
Problem 3
There are 7 boxes and 1743 chocolates. How many chocolates will be in each box?
Each box will have 249 chocolates.
Explanation
To find the chocolates in each box, divide the total chocolates by the number of boxes.
1743/7 = 249
Problem 4
A class has 21 students, and they have 1743 crayons. How many crayons are there for each student?
Each student gets 83 crayons.
Explanation
Dividing the crayons by the total number of students, we will get the number of crayons per student.
1743/21 = 83
Problem 5
1743 apples need to be arranged in 9 baskets. How many apples will go in each basket?
Each of the baskets has 193 apples.
Explanation
Divide the total apples by the number of baskets.
1743/9 = 193
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FAQs on Factors of 1743
1.What are the factors of 1743?
2.Mention the prime factors of 1743.
3.Is 1743 a multiple of 7?
4.Mention the factor pairs of 1743?
5.What is the square of 1743?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1743?
7.What are some fun ways kids in Bahrain can practice Factors of 1743 with numbers?
8.What role do numbers and Factors of 1743 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1743 skills?
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Important Glossaries for Factors of 1743
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1743 are 1, 3, 7, 9, 21, 29, 63, 87, 203, 261, 581, and 1743.
- Prime factors: The factors which are prime numbers. For example, 3, 7, and 29 are prime factors of 1743.
- 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 1743 are (1, 1743), (3, 581), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1743 is 3 × 7 × 29.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number. For example, using this method, 3 × 581 = 1743.
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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
: She loves to read number jokes and games.
