121 LearnersLast updated on May 26th, 2025
Factors of 1709
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 1709, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1709?
The numbers that divide 1709 evenly are known as factors of 1709.
A factor of 1709 is a number that divides the number without remainder.
The factors of 1709 are 1, 11, 31, 61, 341, 1709.
Negative factors of 1709: -1, -11, -31, -61, -341, -1709.
Prime factors of 1709: 11 and 31.
Prime factorization of 1709: 11 × 31 × 5.
The sum of factors of 1709: 1 + 11 + 31 + 61 + 341 + 1709 = 2154
How to Find Factors of 1709?
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 1709. Identifying the numbers which are multiplied to get the number 1709 is the multiplication method.
Step 1: Multiply 1709 by 1, 1709 × 1 = 1709.
Step 2: Check for other numbers that give 1709 after multiplying
11 × 155 = 1709
31 × 55 = 1709
Therefore, the positive factor pairs of 1709 are: (1, 1709), (11, 155), (31, 55).
All these factor pairs result in 1709.
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 simple division method
Step 1: Divide 1709 by 1, 1709 ÷ 1 = 1709.
Step 2: Continue dividing 1709 by the numbers until the remainder becomes 0.
1709 ÷ 1 = 1709
1709 ÷ 11 = 155
1709 ÷ 31 = 55
Therefore, the factors of 1709 are: 1, 11, 31, 61, 341, 1709.
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 1709 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1709 ÷ 11 = 155
155 ÷ 31 = 5
5 ÷ 5 = 1
The prime factors of 1709 are 11 and 31.
The prime factorization of 1709 is: 11 × 31 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1709 is divided by 11 to get 155.
Step 2: Now divide 155 by 31 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1709 is: 11 × 31 × 5.
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 1709: (1, 1709), (11, 155), (31, 55).
Negative factor pairs of 1709: (-1, -1709), (-11, -155), (-31, -55).
Common Mistakes and How to Avoid Them in Factors of 1709
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 1709, 1 and 1709 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 1709 consist of -1, -11, -31, 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 1709/1.5 = 1139.333, 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 1709 are prime numbers.
For example, 11 and 31 are the prime factors of 1709, but it has other factors like 155, 341.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1709 as 11 × 31 × 5 and missing all the key factors.
Factors of 1709 Examples
Problem 1
There are 11 students and 1709 apples. How will they divide it equally?
They will get 155 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of students.
1709/11 = 155
Problem 2
A rectangular garden has a length of 31 meters and a total area of 1709 square meters. Find the width.
55 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1709 = 31 × width
To find the value of width, we need to shift 31 to the left side.
1709/31 = width
Width = 55.
Problem 3
There are 31 gift boxes and 1709 candies. How many candies will be in each box?
Each box will have 55 candies.
Explanation
To find the candies in each box, divide the total candies by the boxes.
1709/31 = 55
Problem 4
In a class, there are 1709 students, and 11 groups. How many students are there in each group?
There are 155 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1709/11 = 155
Problem 5
1709 books need to be arranged in 31 shelves. How many books will go on each shelf?
Each of the shelves has 55 books.
Explanation
Divide total books by shelves.
1709/31 = 55
FAQs on Factors of 1709
1.What are the factors of 1709?
2.Mention the prime factors of 1709.
3.Is 1709 a multiple of 11?
4.Mention the factor pairs of 1709?
5.What is the square of 1709?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1709?
7.What are some fun ways kids in Qatar can practice Factors of 1709 with numbers?
8.What role do numbers and Factors of 1709 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1709 skills?
Important Glossaries for Factor of 1709
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1709 are 1, 11, 31, 61, 341, and 1709.
- Prime factors: The factors which are prime numbers. For example, 11 and 31 are prime factors of 1709.
- 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 1709 are (1, 1709), (11, 155), etc.
- Prime factorization: Breaking down a number into the product of its prime factors. For 1709, it is 11 × 31 × 5.
- Multiples: Numbers that can be divided by another number without a remainder. For example, 1709 is a multiple of 11.
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About BrightChamps in Qatar
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.
