132 LearnersLast updated on May 26th, 2025
Factors of 1736
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 1736, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1736?
The numbers that divide 1736 evenly are known as factors of 1736.
A factor of 1736 is a number that divides the number without remainder.
The factors of 1736 are 1, 2, 4, 8, 13, 16, 26, 52, 67, 104, 134, 268, 536, 868, and 1736.
Negative factors of 1736: -1, -2, -4, -8, -13, -16, -26, -52, -67, -104, -134, -268, -536, -868, -1736.
Prime factors of 1736: 2, 13, and 67.
Prime factorization of 1736: 23 × 13 × 67.
The sum of factors of 1736: 1 + 2 + 4 + 8 + 13 + 16 + 26 + 52 + 67 + 104 + 134 + 268 + 536 + 868 + 1736 = 3845
How to Find Factors of 1736?
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 1736. Identifying the numbers which are multiplied to get the number 1736 is the multiplication method.
Step 1: Multiply 1736 by 1, 1736 × 1 = 1736.
Step 2: Check for other numbers that give 1736 after multiplying
2 × 868 = 1736
4 × 434 = 1736
8 × 217 = 1736
13 × 134 = 1736
16 × 108.5 is not valid as it does not result in a whole number
26 × 67 = 1736
Therefore, the positive factor pairs of 1736 are: (1, 1736), (2, 868), (4, 434), (8, 217), (13, 134), (26, 67).
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 1736 by 1, 1736 ÷ 1 = 1736.
Step 2: Continue dividing 1736 by the numbers until the remainder becomes 0.
1736 ÷ 1 = 1736
1736 ÷ 2 = 868
1736 ÷ 4 = 434
1736 ÷ 8 = 217
1736 ÷ 13 = 134
1736 ÷ 26 = 67
Therefore, the factors of 1736 are: 1, 2, 4, 8, 13, 26, 67, 134, 217, 434, 868, 1736.
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 1736 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1736 ÷ 2 = 868
868 ÷ 2 = 434
434 ÷ 2 = 217
217 ÷ 13 = 167
167 ÷ 67 = 1
The prime factors of 1736 are 2, 13, and 67.
The prime factorization of 1736 is: 23 × 13 × 67.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1736 is divided by 2 to get 868.
Step 2: Now divide 868 by 2 to get 434.
Step 3: Then divide 434 by 2 to get 217.
Step 4: Divide 217 by 13 to get 167.
Step 5: Divide 167 by 67 to get 1. Here, 167 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1736 is: 23 × 13 × 67.
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 1736: (1, 1736), (2, 868), (4, 434), (8, 217), (13, 134), (26, 67).
Negative factor pairs of 1736: (-1, -1736), (-2, -868), (-4, -434), (-8, -217), (-13, -134), (-26, -67).
Common Mistakes and How to Avoid Them in Factors of 1736
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 1736, 1 and 1736 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1736 include -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as well. Only whole numbers can be a factor.
For example, thinking 1.5 is a factor, because 1736/1.5 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 1736 are prime numbers.
For example, 2, 13, and 67 are the prime factors of 1736, but it has other factors like 4, 26.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1736 as 23 × 13 × 67 and missing all the key factors.
Factors of 1736 Examples
Problem 1
There are 868 pieces of fruit and 1736 servings needed. How will they divide it equally?
Each serving will get 2 pieces of fruit.
Explanation
To divide the pieces of fruit equally, we need to divide the total pieces with the number of servings.
1736/868 = 2
Problem 2
A garden is rectangular, the length of the garden is 67 meters, and the total area is 1736 square meters. Find the width?
26 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1736 = 67 × width
To find the value of width, we need to shift 67 to the left side.
1736/67 = width
Width = 26.
Problem 3
There are 217 containers and 1736 items. How many items will be in each container?
Each container will have 8 items.
Explanation
To find the items in each container, divide the total items with the containers.
1736/217 = 8
Problem 4
In a class, there are 1736 students, and 134 groups. How many students are there in each group?
There are 13 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1736/134 = 13
Problem 5
1736 books need to be arranged in 52 shelves. How many books will go on each shelf?
Each of the shelves has 33 books.
Explanation
Divide total books with shelves.
1736/52 = 33
FAQs on Factors of 1736
1.What are the factors of 1736?
2.Mention the prime factors of 1736.
3.Is 1736 a multiple of 4?
4.Mention the factor pairs of 1736?
5.What is the square of 1736?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 1736?
7.What are some fun ways kids in Bahrain can practice Factors of 1736 with numbers?
8.What role do numbers and Factors of 1736 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 1736 skills?
Important Glossaries for Factors of 1736
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1736 are 1, 2, 4, 8, 13, 16, 26, 52, 67, 104, 134, 268, 536, 868, and 1736.
- Prime factors: The factors which are prime numbers. For example, 2, 13, and 67 are prime factors of 1736.
- Prime factorization: Breaking down a number into the product of its prime factors. For example, the prime factorization of 1736 is 23 × 13 × 67.
- 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 1736 are (1, 1736), (2, 868), etc.
- 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.
