114 LearnersLast updated on May 26th, 2025
Factors of 1269
Factors are the numbers that divide any given number evenly without a 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 1269, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1269?
The numbers that divide 1269 evenly are known as factors of 1269. A factor of 1269 is a number that divides the number without a remainder. The factors of 1269 are 1, 3, 13, 39, 423, and 1269.
Negative factors of 1269: -1, -3, -13, -39, -423, and -1269.
Prime factors of 1269: 3 and 13.
Prime factorization of 1269: 3 × 13 × 3 × 13.
The sum of factors of 1269: 1 + 3 + 13 + 39 + 423 + 1269 = 1748
How to Find Factors of 1269?
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 1269. Identifying the numbers which are multiplied to get the number 1269 is the multiplication method.
Step 1: Multiply 1269 by 1, 1269 × 1 = 1269.
Step 2: Check for other numbers that give 1269 after multiplying
3 × 423 = 1269
13 × 39 = 1269
Therefore, the positive factor pairs of 1269 are: (1, 1269), (3, 423), (13, 39). All these factor pairs result in 1269. 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 1269 by 1, 1269 ÷ 1 = 1269.
Step 2: Continue dividing 1269 by the numbers until the remainder becomes 0.
1269 ÷ 1 = 1269
1269 ÷ 3 = 423
1269 ÷ 13 = 39
Therefore, the factors of 1269 are: 1, 3, 13, 39, 423, 1269.
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 1269 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1269 ÷ 3 = 423
423 ÷ 3 = 141
141 ÷ 3 = 47
47 ÷ 47 = 1
The prime factors of 1269 are 3 and 13. The prime factorization of 1269 is: 3 × 13 × 3 × 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, 1269 is divided by 3 to get 423.
Step 2: Now divide 423 by 3 to get 141.
Step 3: Then divide 141 by 3 to get 47. Here, 47 is a prime number, which cannot be divided anymore. So, the prime factorization of 1269 is: 3 × 13 × 3 × 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 1269: (1, 1269), (3, 423), (13, 39).
- Negative factor pairs of 1269: (-1, -1269), (-3, -423), (-13, -39).
Common Mistakes and How to Avoid Them in Factors of 1269
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 1269, 1 and 1269 are also factors.
Factors of 1269 Examples
Problem 1
There are 3 groups of students and 1269 candies. How will they divide it equally?
Each group will get 423 candies.
Explanation
To divide the candies equally, we need to divide the total candies with the number of groups.
1269/3 = 423
Problem 2
A rectangular garden has a length of 13 meters and a total area of 1269 square meters. Find the width.
The width is 97.615 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1269 = 13 × width
To find the value of width, we need to shift 13 to the left side.
1269/13 = width
Width ≈ 97.615
Problem 3
There are 39 boxes and 1269 apples. How many apples will be in each box?
Each box will have 32.538 apples.
Explanation
To find the apples in each box, divide the total apples with the number of boxes.
1269/39 ≈ 32.538
Problem 4
In a choir, there are 1269 singers and 13 sections. How many singers are there in each section?
There are 97.615 singers in each section.
Explanation
Dividing the singers by the total sections, we will get the number of singers in each section.
1269/13 ≈ 97.615
Problem 5
1269 books need to be arranged in 39 shelves. How many books will go on each shelf?
Each of the shelves has 32.538 books.
Explanation
Divide total books by shelves. 1269/39 ≈ 32.538
FAQs on Factors of 1269
1.What are the factors of 1269?
2.Mention the prime factors of 1269.
3.Is 1269 a multiple of 3?
4.Mention the factor pairs of 1269?
5.What is the square of 1269?
Important Glossaries for Factor of 1269
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1269 are 1, 3, 13, 39, 423, and 1269.
- Prime factors: The factors which are prime numbers. For example, 3 and 13 are prime factors of 1269.
- 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 1269 are (1, 1269), (3, 423), etc.
- Prime factorization: Breaking down a number into its prime factors, for example, the prime factorization of 1269 is 3 × 13 × 3 × 13.
- Multiple: A number that can be divided by another number without a remainder, for example, 1269 is a multiple of 3.
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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
: She loves to read number jokes and games.
