142 LearnersLast updated on May 28th, 2025
Factors of 1309
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 1309, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1309?
The numbers that divide 1309 evenly are known as factors of 1309.
A factor of 1309 is a number that divides the number without remainder.
The factors of 1309 are 1, 7, 11, 13, 77, 91, 143, and 1309.
Negative factors of 1309: -1, -7, -11, -13, -77, -91, -143, and -1309.
Prime factors of 1309: 7, 11, and 13.
Prime factorization of 1309: 7 × 11 × 13.
The sum of factors of 1309: 1 + 7 + 11 + 13 + 77 + 91 + 143 + 1309 = 1652
How to Find Factors of 1309?
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 1309. Identifying the numbers which are multiplied to get the number 1309 is the multiplication method.
Step 1: Multiply 1309 by 1, 1309 × 1 = 1309.
Step 2: Check for other numbers that give 1309 after multiplying
7 × 187 = 1309
11 × 119 = 1309
13 × 101 = 1309
Therefore, the positive factor pairs of 1309 are: (1, 1309), (7, 187), (11, 119), (13, 101).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 1309 by 1, 1309 ÷ 1 = 1309.
Step 2: Continue dividing 1309 by the numbers until the remainder becomes 0.
1309 ÷ 1 = 1309
1309 ÷ 7 = 187
1309 ÷ 11 = 119
1309 ÷ 13 = 101
Therefore, the factors of 1309 are: 1, 7, 11, 13, 77, 91, 143, 1309.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 1309 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1309 ÷ 7 = 187
187 ÷ 11 = 17
17 ÷ 13 = 1
The prime factors of 1309 are 7, 11, and 13.
The prime factorization of 1309 is: 7 × 11 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1309 is divided by 7 to get 187.
Step 2: Now divide 187 by 11 to get 17.
Step 3: Then divide 17 by 13 to get 1.
Here, 13 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1309 is: 7 × 11 × 13.
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 1309: (1, 1309), (7, 187), (11, 119), (13, 101).
Negative factor pairs of 1309: (-1, -1309), (-7, -187), (-11, -119), (-13, -101).
Common Mistakes and How to Avoid Them in Factors of 1309
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 1309, 1 and 1309 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 1309 consist of -1, -7, -11, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1309/1.5 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 1309 are prime numbers. For example, 7, 11, and 13 are the prime factors of 1309, but it has other factors like 77, 91.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1309 as 7 × 11 × 13 and missing all the key factors.
Factors of 1309 Examples
Problem 1
There are 13 students and 1309 books. How will they divide it equally?
They will get 101 books each.
Explanation
To divide the books equally, we need to divide the total books by the number of students.
1309/13 = 101
Problem 2
A garden is rectangular, the length of the garden is 11 meters, and the total area is 1309 square meters. Find the width.
119 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1309 = 11 × width
To find the value of width, we need to shift 11 to the left side.
1309/11 = width
Width = 119.
Problem 3
There are 143 bags and 1309 apples. How many apples will be in each bag?
Each bag will have 9 apples.
Explanation
To find the apples in each bag, divide the total apples by the bags.
1309/143 = 9
Problem 4
In a class, there are 1309 students, and 91 groups. How many students are there in each group?
There are 14 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1309/91 = 14
Problem 5
1309 papers need to be arranged in 13 stacks. How many papers will go on each stack?
Each of the stacks has 101 papers.
Explanation
Divide total papers by stacks.
1309/13 = 101
FAQs on Factors of 1309
1.What are the factors of 1309?
2.Mention the prime factors of 1309.
3.Is 1309 a multiple of 7?
4.Mention the factor pairs of 1309.
5.What is the sum of the factors of 1309?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 1309?
7.What are some fun ways kids in Vietnam can practice Factors of 1309 with numbers?
8.What role do numbers and Factors of 1309 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 1309 skills?
Important Glossaries for Factors of 1309
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1309 are 1, 7, 11, 13, 77, 91, 143, and 1309.
- Prime factors: The factors which are prime numbers. For example, 7, 11, and 13 are prime factors of 1309.
- 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 1309 are (1, 1309), (7, 187), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1309 is 7 × 11 × 13.
- Negative factors: Factors of a number that are negative. For example, the negative factors of 1309 are -1, -7, -11, -13, -77, -91, -143, and -1309.
Explore More numbers
About BrightChamps in Vietnam
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.
