100 LearnersLast updated on May 26th, 2025
Factors of 1744
Factors are the numbers that divide any given number evenly without a 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 1744, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1744?
The numbers that divide 1744 evenly are known as factors of 1744.
A factor of 1744 is a number that divides the number without a remainder.
The factors of 1744 are 1, 2, 4, 8, 16, 109, 218, 436, 872, and 1744.
Negative factors of 1744: -1, -2, -4, -8, -16, -109, -218, -436, -872, and -1744.
Prime factors of 1744: 2 and 109.
Prime factorization of 1744: 23 × 109.
The sum of factors of 1744: 1 + 2 + 4 + 8 + 16 + 109 + 218 + 436 + 872 + 1744 = 3410
How to Find Factors of 1744?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 1744. Identifying the numbers which are multiplied to get the number 1744 is the multiplication method.
Step 1: Multiply 1744 by 1, 1744 × 1 = 1744.
Step 2: Check for other numbers that give 1744 after multiplying
2 × 872 = 1744
4 × 436 = 1744
8 × 218 = 1744
16 × 109 = 1744
Therefore, the positive factor pairs of 1744 are: (1, 1744), (2, 872), (4, 436), (8, 218), (16, 109).
All these factor pairs result in 1744.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 1744 by 1, 1744 ÷ 1 = 1744.
Step 2: Continue dividing 1744 by the numbers until the remainder becomes 0.
1744 ÷ 1 = 1744
1744 ÷ 2 = 872
1744 ÷ 4 = 436
1744 ÷ 8 = 218
1744 ÷ 16 = 109
Therefore, the factors of 1744 are: 1, 2, 4, 8, 16, 109, 218, 436, 872, 1744.
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 1744 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1744 ÷ 2 = 872
872 ÷ 2 = 436
436 ÷ 2 = 218
218 ÷ 2 = 109
109 ÷ 109 = 1
The prime factors of 1744 are 2 and 109.
The prime factorization of 1744 is: 23 × 109.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1744 is divided by 2 to get 872.
Step 2: Now divide 872 by 2 to get 436.
Step 3: Then divide 436 by 2 to get 218.
Step 4: Divide 218 by 2 to get 109. Here, 109 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1744 is: 23 × 109.
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 1744: (1, 1744), (2, 872), (4, 436), (8, 218), and (16, 109).
Negative factor pairs of 1744: (-1, -1744), (-2, -872), (-4, -436), (-8, -218), and (-16, -109).
Common Mistakes and How to Avoid Them in Factors of 1744
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1744, 1 and 1744 is also a factor.
Factors of 1744 Examples
Problem 1
There are 4 friends and 1744 candies. How will they divide it equally?
They will get 436 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
1744/4 = 436
Problem 2
A garden is rectangular, the length of the garden is 16 meters and the total area is 1744 square meters. Find the width?
109 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1744 = 16 × width
To find the value of width, we need to shift 16 to the left side.
1744/16 = width
Width = 109.
Problem 3
There are 8 baskets and 1744 apples. How many apples will be in each basket?
Each basket will have 218 apples.
Explanation
To find the apples in each basket, divide the total apples with the baskets.
1744/8 = 218
Problem 4
In a class, there are 1744 students, and 16 groups. How many students are there in each group?
There are 109 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1744/16 = 109
Problem 5
1744 plants need to be arranged in 2 rows. How many plants will go in each row?
Each of the rows has 872 plants.
Explanation
Divide total plants with rows.
1744/2 = 872
FAQs on Factors of 1744
1.What are the factors of 1744?
2.Mention the prime factors of 1744.
3.Is 1744 a multiple of 8?
4.Mention the factor pairs of 1744?
5.What is the cube of 1744?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1744?
7.What are some fun ways kids in Bahrain can practice Factors of 1744 with numbers?
8.What role do numbers and Factors of 1744 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1744 skills?
Important Glossaries for Factor of 1744
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1744 are 1, 2, 4, 8, 16, 109, 218, 436, 872, and 1744.
- Prime factors: The factors which are prime numbers. For example, 2 and 109 are prime factors of 1744.
- 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 1744 are (1, 1744), (2, 872), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1744 is 23 × 109.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
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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.
