132 LearnersLast updated on May 26th, 2025
Factors of 1748
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 1748, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1748?
The numbers that divide 1748 evenly are known as factors of 1748.
A factor of 1748 is a number that divides the number without remainder.
The factors of 1748 are 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 349, 532, 698, 1748.
Negative factors of 1748: -1, -2, -4, -7, -14, -19, -28, -38, -76, -133, -266, -349, -532, -698, -1748.
Prime factors of 1748: 2, 7, and 19.
Prime factorization of 1748: 2 × 2 × 7 × 19.
The sum of factors of 1748: 1 + 2 + 4 + 7 + 14 + 19 + 28 + 38 + 76 + 133 + 266 + 349 + 532 + 698 + 1748 = 3926
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How to Find Factors of 1748?
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 1748. Identifying the numbers which are multiplied to get the number 1748 is the multiplication method.
Step 1: Multiply 1748 by 1, 1748 × 1 = 1748.
Step 2: Check for other numbers that give 1748 after multiplying
2 × 874 = 1748
4 × 437 = 1748
7 × 249 = 1748
14 × 124 = 1748
19 × 92 = 1748
28 × 62 = 1748
38 × 46 = 1748
Therefore, the positive factor pairs of 1748 are: (1, 1748), (2, 874), (4, 437), (7, 249), (14, 124), (19, 92), (28, 62), (38, 46).
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 1748 by 1, 1748 ÷ 1 = 1748.
Step 2: Continue dividing 1748 by the numbers until the remainder becomes 0.
1748 ÷ 1 = 1748
1748 ÷ 2 = 874
1748 ÷ 4 = 437
1748 ÷ 7 = 249
1748 ÷ 14 = 124
1748 ÷ 19 = 92
1748 ÷ 28 = 62
1748 ÷ 38 = 46
Therefore, the factors of 1748 are: 1, 2, 4, 7, 14, 19, 28, 38, 46, 62, 92, 124, 249, 437, 874, 1748.
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 1748 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1748 ÷ 2 = 874
874 ÷ 2 = 437
437 ÷ 7 = 62.428 (not whole, so divide by next prime)
437 ÷ 19 = 23
23 ÷ 23 = 1
The prime factors of 1748 are 2, 7, and 19.
The prime factorization of 1748 is: 2 × 2 × 7 × 19.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1748 is divided by 2 to get 874.
Step 2: Now divide 874 by 2 to get 437.
Step 3: Divide 437 by 19 to get 23. Here, 23 is a prime number, that cannot be divided anymore.
So, the prime factorization of 1748 is: 2 × 2 × 7 × 19.
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 1748: (1, 1748), (2, 874), (4, 437), (7, 249), (14, 124), (19, 92), (28, 62), (38, 46).
Negative factor pairs of 1748: (-1, -1748), (-2, -874), (-4, -437), (-7, -249), (-14, -124), (-19, -92), (-28, -62), (-38, -46).
Common Mistakes and How to Avoid Them in Factors of 1748
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 number. Always remember to include 1 and the number itself.
For example, in factors of 1748, 1 and 1748 is also a factor.
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 1748 consist of -1, -2, -4, 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 1748/1.5 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 1748 are prime numbers.
For example, 2, 7, and 19 are the prime factors of 1748, but it has other factors like 4, 28.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1748 as 2 × 2 × 7 × 19 and missing all the key factors.
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Factors of 1748 Examples
Problem 1
There are 14 students and 1748 candies. How will they divide it equally?
They will get 124 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of students.
1748/14 = 124
Problem 2
A rectangular garden has a length of 38 meters and a total area of 1748 square meters. What is the width?
46 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1748 = 38 × width
To find the value of width, we need to shift 38 to the left side.
1748/38 = width
Width = 46.
Problem 3
There are 92 packages and 1748 items. How many items will be in each package?
Each package will have 19 items.
Explanation
To find the items in each package, divide the total items with the packages.
1748/92 = 19
Problem 4
In a warehouse, there are 1748 boxes, and 7 sections. How many boxes are there in each section?
There are 249 boxes in each section.
Explanation
Dividing the boxes with the total sections, we will get the number of boxes in each section.
1748/7 = 249
Problem 5
1748 books need to be distributed into 38 shelves. How many books will go on each shelf?
Each of the shelves has 46 books.
Explanation
Divide total books with shelves.
1748/38 = 46
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FAQs on Factors of 1748
1.What are the factors of 1748?
2.Mention the prime factors of 1748.
3.Is 1748 a multiple of 14?
4.Mention the factor pairs of 1748?
5.What is the square of 1748?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1748?
7.What are some fun ways kids in Bahrain can practice Factors of 1748 with numbers?
8.What role do numbers and Factors of 1748 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1748 skills?
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Important Glossaries for Factors of 1748
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1748 are 1, 2, 4, 7, 14, 19, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 7, and 19 are prime factors of 1748.
- 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 1748 are (1, 1748), (2, 874), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1748 is 2 × 2 × 7 × 19.
- Multiples: Numbers that are the product of a given number and an integer. For example, 1748 is a multiple of 14.
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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.
