119 LearnersLast updated on May 26th, 2025
Factors of 1719
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 1719, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1719?
The numbers that divide 1719 evenly are known as factors of 1719.
A factor of 1719 is a number that divides the number without remainder.
The factors of 1719 are 1, 3, 17, 33, 57, 1719.
Negative factors of 1719: -1, -3, -17, -33, -57, -1719.
Prime factors of 1719: 3 and 19.
Prime factorization of 1719: 3 × 19 × 3 × 3.
The sum of factors of 1719: 1 + 3 + 17 + 33 + 57 + 1719 = 1830
How to Find Factors of 1719?
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 1719. Identifying the numbers which are multiplied to get the number 1719 is the multiplication method.
Step 1: Multiply 1719 by 1, 1719 × 1 = 1719.
Step 2: Check for other numbers that give 1719 after multiplying
3 × 573 = 1719
17 × 101 = 1719
19 × 90 = 1719
Therefore, the positive factor pairs of 1719 are: (1, 1719), (3, 573), (17, 101), (19, 90).
All these factor pairs result in 1719.
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 1719 by 1, 1719 ÷ 1 = 1719.
Step 2: Continue dividing 1719 by the numbers until the remainder becomes 0.
1719 ÷ 1 = 1719
1719 ÷ 3 = 573
1719 ÷ 17 = 101
1719 ÷ 19 = 90
Therefore, the factors of 1719 are: 1, 3, 17, 33, 57, 1719.
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 1719 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1719 ÷ 3 = 573
573 ÷ 3 = 191
191 ÷ 17 = 11
11 ÷ 11 = 1
The prime factors of 1719 are 3, 19, and 11.
The prime factorization of 1719 is: 3 × 19 × 3 × 3.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1719 is divided by 3 to get 573.
Step 2: Now divide 573 by 3 to get 191.
Step 3: Then divide 191 by 17 to get 11. Here, 11 is a prime number and cannot be divided further. So, the prime factorization of 1719 is: 3 × 19 × 3 × 3.
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 1719: (1, 1719), (3, 573), (17, 101), and (19, 90).
Negative factor pairs of 1719: (-1, -1719), (-3, -573), (-17, -101), and (-19, -90).
Common Mistakes and How to Avoid Them in Factors of 1719
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 1719, 1 and 1719 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 1719 include -1, -3, -17, 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 1719/1.5 = 1146, 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 1719 are prime numbers.
For example, 3 and 19 are the prime factors of 1719, but it has other factors like 17, 101.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1719 as 3 × 19 × 3 × 3 and missing all the key factors.
Factors of 1719 Examples
Problem 1
A gardener has 1719 seeds and wants to plant them in 19 rows. How many seeds will each row have?
Each row will have 90 seeds.
Explanation
To divide the seeds equally, we need to divide the total seeds by the number of rows.
1719/19 = 90
Problem 2
A rectangular garden has an area of 1719 square meters and a width of 17 meters. What is the length of the garden?
The length is 101 meters.
Explanation
To find the length of the garden, we use the formula:
Area = length × width
1719 = length × 17
To find the value of length, we need to shift 17 to the left side.
1719/17 = length
Length = 101.
Problem 3
A library has 1719 books and wants to arrange them equally on 3 shelves. How many books will each shelf have?
Each shelf will have 573 books.
Explanation
To find the books on each shelf, divide the total books by the number of shelves.
1719/3 = 573
Problem 4
A teacher has 1719 paper sheets and wants to distribute them among 33 students. How many paper sheets will each student get?
Each student will get 52 paper sheets.
Explanation
Dividing the paper sheets by the number of students, we will get the number of sheets each student gets.
1719/33 = 52
Problem 5
1719 marbles need to be packed into 57 boxes. How many marbles will go in each box?
Each box will have 30 marbles.
Explanation
Divide the total marbles by the number of boxes.
1719/57 = 30
FAQs on Factors of 1719
1.What are the factors of 1719?
2.Mention the prime factors of 1719.
3.Is 1719 a multiple of 3?
4.Mention the factor pairs of 1719?
5.What is the square of 1719?
6.How can children in India use numbers in everyday life to understand Factors of 1719?
7.What are some fun ways kids in India can practice Factors of 1719 with numbers?
8.What role do numbers and Factors of 1719 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 1719 skills?
Important Glossaries for Factors of 1719
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1719 are 1, 3, 17, 33, 57, and 1719.
- Prime factors: The factors which are prime numbers. For example, 3 and 19 are prime factors of 1719.
- 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 1719 are (1, 1719), (3, 573), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1719 is 3 × 19 × 3 × 3.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the target number. For example, using multiplication to find factor pairs of 1719.
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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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