Last updated on May 26th, 2025
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.
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
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 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.
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.
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 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.
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).
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 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.
To divide the parts equally, we need to divide the total parts by the number of sections.
1734/6 = 289
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.
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
There are 102 people and 1734 seats in a theater. How many seats will each person have?
Each person will have approximately 17 seats.
To find the seats per person, divide the total seats by the number of people.
1734/102 ≈ 17
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.
Dividing the students with the total groups, we will get the number of students in each group.
1734/34 = 51
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.
Divide total books by shelves.
1734/58 ≈ 29.896
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.