139 LearnersLast updated on May 26th, 2025
Factors of 1734
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 1734, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1734?
The numbers that divide 1734 evenly are known as factors of 1734.
A factor of 1734 is a number that divides the number without remainder.
The factors of 1734 are 1, 2, 3, 6, 17, 18, 29, 34, 51, 58, 87, 102, 174, 289, 867, and 1734.
Negative factors of 1734: -1, -2, -3, -6, -17, -18, -29, -34, -51, -58, -87, -102, -174, -289, -867, and -1734.
Prime factors of 1734: 2, 3, 17, and 29.
Prime factorization of 1734: 2 × 3 × 17 × 29.
The sum of factors of 1734: 1 + 2 + 3 + 6 + 17 + 18 + 29 + 34 + 51 + 58 + 87 + 102 + 174 + 289 + 867 + 1734 = 3472
How to Find Factors of 1734?
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 1734. Identifying the numbers which are multiplied to get the number 1734 is the multiplication method.
Step 1: Multiply 1734 by 1, 1734 × 1 = 1734.
Step 2: Check for other numbers that give 1734 after multiplying
2 × 867 = 1734
3 × 578 = 1734
6 × 289 = 1734
17 × 102 = 1734
18 × 96.333 = 1734 (not a factor as result is not a whole number)
29 × 59.793 = 1734 (not a factor as result is not a whole number)
Therefore, the positive factor pairs of 1734 are: (1, 1734), (2, 867), (3, 578), (6, 289), (17, 102).
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 1734 by 1, 1734 ÷ 1 = 1734.
Step 2: Continue dividing 1734 by the numbers until the remainder becomes 0.
1734 ÷ 1 = 1734
1734 ÷ 2 = 867
1734 ÷ 3 = 578
1734 ÷ 6 = 289
1734 ÷ 17 = 102
Therefore, the factors of 1734 are: 1, 2, 3, 6, 17, 18, 29, 34, 51, 58, 87, 102, 174, 289, 867, 1734.
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 1734 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1734 ÷ 2 = 867
867 ÷ 3 = 289
289 ÷ 17 = 17
17 ÷ 17 = 1
The prime factors of 1734 are 2, 3, 17, and 29.
The prime factorization of 1734 is: 2 × 3 × 17 × 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, 1734 is divided by 2 to get 867.
Step 2: Now divide 867 by 3 to get 289.
Step 3: Then divide 289 by 17 to get 17.
Step 4: Divide 17 by 17 to get 1. Here, 17 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1734 is: 2 × 3 × 17 × 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 1734: (1, 1734), (2, 867), (3, 578), (6, 289), (17, 102).
Negative factor pairs of 1734: (-1, -1734), (-2, -867), (-3, -578), (-6, -289), (-17, -102).
Common Mistakes and How to Avoid Them in Factors of 1734
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 1734, 1 and 1734 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 1734 consist of -1, -2, -3, 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, because 1734/1.5 = 1156, 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 1734 are prime numbers.
For example, 2, 3, 17, and 29 are the prime factors of 1734, but it has other factors like 6, 102.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1734 as 2 × 3 × 17 × 29 and missing all the key factors.
Factors of 1734 Examples
Problem 1
A vehicle has 1734 parts and needs to be divided into 6 sections equally. How many parts will each section have?
Each section will have 289 parts.
Explanation
To divide the parts equally, we need to divide the total parts by the number of sections.
1734/6 = 289
Problem 2
A garden is rectangular, the length of the garden is 29 meters and the total area is 1734 square meters. Find the width?
The width is 59.793 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1734 = 29 × width
To find the value of width, we need to shift 29 to the left side.
1734/29 = width Width ≈ 59.793
Problem 3
There are 102 people and 1734 seats in a theater. How many seats will each person have?
Each person will have approximately 17 seats.
Explanation
To find the seats per person, divide the total seats by the number of people.
1734/102 ≈ 17
Problem 4
In a class, there are 1734 students, and 34 groups. How many students are there in each group?
There are 51 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1734/34 = 51
Problem 5
1734 books need to be arranged in 58 shelves. How many books will go on each shelf?
Each of the shelves has 29.896 books.
Explanation
Divide total books by shelves.
1734/58 ≈ 29.896
FAQs on Factors of 1734
1.What are the factors of 1734?
2.Mention the prime factors of 1734.
3.Is 1734 a multiple of 6?
4.Mention the factor pairs of 1734?
5.What is the square of 1734?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1734?
7.What are some fun ways kids in Bahrain can practice Factors of 1734 with numbers?
8.What role do numbers and Factors of 1734 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1734 skills?
Important Glossaries for Factor of 1734
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1734 are 1, 2, 3, 6, 17, 18, 29, 34, 51, 58, 87, 102, 174, 289, 867, 1734.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 17, and 29 are prime factors of 1734.
- 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 1734 are (1, 1734), (2, 867), etc.
- Prime factorization: Breaking down a number into its prime factors multiplied together. For example, 2 × 3 × 17 × 29 is the prime factorization of 1734.
- Multiple: A multiple of a number is the product of that number and an integer. For example, 1734 is a multiple of 6.
Explore More numbers
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.
