136 LearnersLast updated on May 26th, 2025
Factors of 1729
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 1729, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1729?
The numbers that divide 1729 evenly are known as factors of 1729.
A factor of 1729 is a number that divides the number without remainder.
The factors of 1729 are 1, 7, 13, 19, 91, 133, 247, and 1729.
Negative factors of 1729: -1, -7, -13, -19, -91, -133, -247, and -1729.
Prime factors of 1729: 7, 13, and 19.
Prime factorization of 1729: 7 × 13 × 19.
The sum of factors of 1729: 1 + 7 + 13 + 19 + 91 + 133 + 247 + 1729 = 2240
How to Find Factors of 1729?
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 1729. Identifying the numbers which are multiplied to get the number 1729 is the multiplication method.
Step 1: Multiply 1729 by 1, 1729 × 1 = 1729.
Step 2: Check for other numbers that give 1729 after multiplying
7 × 247 = 1729
13 × 133 = 1729
19 × 91 = 1729
Therefore, the positive factor pairs of 1729 are: (1, 1729), (7, 247), (13, 133), (19, 91).
All these factor pairs result in 1729.
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 1729 by 1, 1729 ÷ 1 = 1729.
Step 2: Continue dividing 1729 by the numbers until the remainder becomes 0.
1729 ÷ 1 = 1729
1729 ÷ 7 = 247
1729 ÷ 13 = 133
1729 ÷ 19 = 91
Therefore, the factors of 1729 are: 1, 7, 13, 19, 91, 133, 247, 1729.
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 1729 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1729 ÷ 7 = 247
247 ÷ 13 = 19
19 ÷ 19 = 1
The prime factors of 1729 are 7, 13, and 19.
The prime factorization of 1729 is: 7 × 13 × 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, 1729 is divided by 7 to get 247.
Step 2: Now divide 247 by 13 to get 19.
Step 3: Divide 19 by 19 to get 1. Here, 19 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1729 is: 7 × 13 × 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 1729: (1, 1729), (7, 247), (13, 133), and (19, 91).
Negative factor pairs of 1729: (-1, -1729), (-7, -247), (-13, -133), and (-19, -91).
Common Mistakes and How to Avoid Them in Factors of 1729
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 1729, 1 and 1729 are also factors.
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 1729 consist of -1, -7, -13, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1729/1.5 = 1152.666..., and it 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 1729 are prime numbers.
For example, 7, 13, and 19 are the prime factors of 1729, but it has other factors like 91 and 133.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing the wrong factors.
For example, not breaking 1729 as 7 × 13 × 19 and missing all the key factors.
Factors of 1729 Examples
Problem 1
There are 19 boxes of chocolates and 1729 chocolates in total. How many chocolates will go in each box?
Each box will have 91 chocolates.
Explanation
To divide the chocolates equally, we need to divide the total chocolates by the number of boxes.
1729/19 = 91
Problem 2
A plot of land is rectangular, the length of the plot is 13 meters and the total area is 1729 square meters. Find the width?
133 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
1729 = 13 × width
To find the value of width, we need to shift 13 to the left side.
1729/13 = width
Width = 133.
Problem 3
There are 247 gift bags and 1729 candies. How many candies will be in each bag?
Each bag will have 7 candies.
Explanation
To find the candies in each bag, divide the total candies by the bags.
1729/247 = 7
Problem 4
In a theater, there are 1729 seats, and 7 sections. How many seats are there in each section?
There are 247 seats in each section.
Explanation
Dividing the seats by the total sections, we will get the number of seats in each section.
1729/7 = 247
Problem 5
1729 pages need to be read over 91 days. How many pages will be read each day?
Each day, 19 pages will be read.
Explanation
Divide total pages by days.
1729/91 = 19
FAQs on Factors of 1729
1.What are the factors of 1729?
2.Mention the prime factors of 1729.
3.Is 1729 a multiple of 13?
4.Mention the factor pairs of 1729?
5.What is the square of 1729?
6.How can children in India use numbers in everyday life to understand Factors of 1729?
7.What are some fun ways kids in India can practice Factors of 1729 with numbers?
8.What role do numbers and Factors of 1729 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 1729 skills?
Important Glossaries for Factors of 1729
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1729 are 1, 7, 13, 19, 91, 133, 247, and 1729.
- Prime factors: The factors which are prime numbers. For example, 7, 13, and 19 are prime factors of 1729.
- 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 1729 are (1, 1729), (7, 247), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For 1729, it is 7 × 13 × 19.
- Negative factors: The negative counterparts of positive factors. For example, -1, -7, -13, etc., are negative factors of 1729.
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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
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