101 LearnersLast updated on May 26th, 2025
Factors of 1746
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 1746, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1746?
The numbers that divide 1746 evenly are known as factors of 1746.
A factor of 1746 is a number that divides the number without remainder.
The factors of 1746 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 291, 523, 873, and 1746.
Negative factors of 1746: -1, -2, -3, -6, -9, -13, -18, -26, -27, -39, -54, -78, -117, -234, -291, -523, -873, and -1746.
Prime factors of 1746: 2, 3, and 97.
Prime factorization of 1746: 2 × 33 × 97.
The sum of factors of 1746: 1 + 2 + 3 + 6 + 9 + 13 + 18 + 26 + 27 + 39 + 54 + 78 + 117 + 234 + 291 + 523 + 873 + 1746 = 4060
How to Find Factors of 1746?
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 1746. Identifying the numbers which are multiplied to get the number 1746 is the multiplication method.
Step 1: Multiply 1746 by 1, 1746 × 1 = 1746.
Step 2: Check for other numbers that give 1746 after multiplying
2 × 873 = 1746
3 × 582 = 1746
6 × 291 = 1746
9 × 194 = 1746
13 × 134 = 1746
18 × 97 = 1746
Therefore, the positive factor pairs of 1746 are: (1, 1746), (2, 873), (3, 582), (6, 291), (9, 194), (13, 134), and (18, 97).
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 a simple division method:
Step 1: Divide 1746 by 1, 1746 ÷ 1 = 1746.
Step 2: Continue dividing 1746 by the numbers until the remainder becomes 0.
1746 ÷ 1 = 1746
1746 ÷ 2 = 873
1746 ÷ 3 = 582
1746 ÷ 6 = 291
1746 ÷ 9 = 194
1746 ÷ 13 = 134
1746 ÷ 18 = 97
Therefore, the factors of 1746 are: 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 291, 523, 873, and 1746.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 1746 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1746 ÷ 2 = 873
873 ÷ 3 = 291
291 ÷ 3 = 97
97 ÷ 97 = 1
The prime factors of 1746 are 2, 3, and 97.
The prime factorization of 1746 is: 2 × 33 × 97.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 1746 is divided by 2 to get 873.
Step 2: Now divide 873 by 3 to get 291.
Step 3: Then divide 291 by 3 to get 97.
Step 4: Divide 97 by 97 to get 1. Here, 97 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1746 is: 2 × 33 × 97.
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 1746: (1, 1746), (2, 873), (3, 582), (6, 291), (9, 194), (13, 134), and (18, 97).
Negative factor pairs of 1746: (-1, -1746), (-2, -873), (-3, -582), (-6, -291), (-9, -194), (-13, -134), and (-18, -97).
Common Mistakes and How to Avoid Them in Factors of 1746
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 whole number. Always remember to include 1 and the number itself.
For example, in factors of 1746, 1 and 1746 is also a factor.
Factors of 1746 Examples
Problem 1
There are 3 friends and 1746 candies. How will they divide it equally?
They will get 582 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
1746/3 = 582
Problem 2
A field is rectangular, the length of the field is 97 meters and the total area is 1746 square meters. Find the width?
18 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1746 = 97 × width
To find the value of width, we need to shift 97 to the left side.
1746/97 = width
Width = 18.
Problem 3
There are 6 bags and 1746 marbles. How many marbles will be in each bag?
Each bag will have 291 marbles.
Explanation
To find the marbles in each bag, divide the total marbles by the bags.
1746/6 = 291
Problem 4
In a class, there are 1746 students, and 9 groups. How many students are there in each group?
There are 194 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1746/9 = 194
Problem 5
1746 books need to be arranged in 27 shelves. How many books will go on each shelf?
Each of the shelves has 64 books.
Explanation
Divide total books by shelves.
1746/27 = 64.6667; round down to 64 since books must be whole numbers.
FAQs on Factors of 1746
1.What are the factors of 1746?
2.Mention the prime factors of 1746.
3.Is 1746 a multiple of 9?
4.Mention the factor pairs of 1746?
5.What is the square of 1746?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1746?
7.What are some fun ways kids in Bahrain can practice Factors of 1746 with numbers?
8.What role do numbers and Factors of 1746 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1746 skills?
Important Glossaries for Factors of 1746
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1746 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 291, 523, 873, and 1746.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 97 are prime factors of 1746.
- 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 1746 are (1, 1746), (2, 873), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1746 is 2 × 33 × 97.
- Multiple: A multiple of a number is the product of that number and any integer. For example, 1746 is a multiple of 9.
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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.
