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Last updated on May 26th, 2025

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Factors of 1729

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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.

Factors of 1729 for Australian Students
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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

factors of 1729

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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
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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.

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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.

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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.

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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).

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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

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Forgetting the number itself and 1 is a factor

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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.

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Factors of 1729 Examples

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Problem 1

There are 19 boxes of chocolates and 1729 chocolates in total. How many chocolates will go in each box?

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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

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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?

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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.

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Problem 3

There are 247 gift bags and 1729 candies. How many candies will be in each bag?

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Each bag will have 7 candies.

Explanation

To find the candies in each bag, divide the total candies by the bags.

1729/247 = 7

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Problem 4

In a theater, there are 1729 seats, and 7 sections. How many seats are there in each section?

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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

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Problem 5

1729 pages need to be read over 91 days. How many pages will be read each day?

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Each day, 19 pages will be read.

Explanation

Divide total pages by days.

1729/91 = 19

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FAQs on Factors of 1729

1.What are the factors of 1729?

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2.Mention the prime factors of 1729.

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3.Is 1729 a multiple of 13?

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4.Mention the factor pairs of 1729?

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5.What is the square of 1729?

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6.How can children in Australia use numbers in everyday life to understand Factors of 1729?

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7.What are some fun ways kids in Australia can practice Factors of 1729 with numbers?

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8.What role do numbers and Factors of 1729 play in helping children in Australia develop problem-solving skills?

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9.How can families in Australia create number-rich environments to improve Factors of 1729 skills?

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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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About BrightChamps in Australia

At BrightChamps, numbers mean more than just digits—they open doors to a world of possibilities! We’re here to help children across Australia grasp essential math skills, focusing today on Factors of 1729 with a special emphasis on factors—in a way that’s fun, engaging, and easy to follow. Whether your child is figuring out the speed of a roller coaster at Luna Park Sydney, keeping score at a local cricket match, or managing their allowance to buy gadgets, understanding numbers builds everyday confidence. Our hands-on lessons make learning enjoyable and straightforward. Since kids in Australia learn differently, we customize lessons to suit each child’s style. From Sydney’s vibrant streets to the beautiful Gold Coast beaches, BrightChamps brings math to life throughout Australia. Let’s make factors an exciting part of every child’s math journey!
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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.

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Fun Fact

: She loves to read number jokes and games.

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