Last updated on May 30th, 2025
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 1209, how they are used in real life, and tips to learn them quickly.
The numbers that divide 1209 evenly are known as factors of 1209.
A factor of 1209 is a number that divides the number without a remainder.
The factors of 1209 are 1, 3, 13, 39, 31, 93, 403, and 1209.
Negative factors of 1209: -1, -3, -13, -31, -39, -93, -403, and -1209.
Prime factors of 1209: 3, 13, and 31.
Prime factorization of 1209: 3 × 13 × 31.
The sum of factors of 1209: 1 + 3 + 13 + 31 + 39 + 93 + 403 + 1209 = 1792
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1209. Identifying the numbers which are multiplied to get the number 1209 is the multiplication method.
Step 1: Multiply 1209 by 1, 1209 × 1 = 1209.
Step 2: Check for other numbers that give 1209 after multiplying
3 × 403 = 1209
13 × 93 = 1209
31 × 39 = 1209
Therefore, the positive factor pairs of 1209 are: (1, 1209), (3, 403), (13, 93), (31, 39). For every positive factor, there is a negative factor.
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 1209 by 1, 1209 ÷ 1 = 1209.
Step 2: Continue dividing 1209 by the numbers until the remainder becomes 0.
1209 ÷ 1 = 1209
1209 ÷ 3 = 403
1209 ÷ 13 = 93
1209 ÷ 31 = 39
Therefore, the factors of 1209 are: 1, 3, 13, 31, 39, 93, 403, 1209.
The factors can be found by dividing them by prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 1209 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1209 ÷ 3 = 403
403 ÷ 13 = 31
31 ÷ 31 = 1
The prime factors of 1209 are 3, 13, and 31.
The prime factorization of 1209 is: 3 × 13 × 31.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1209 is divided by 3 to get 403.
Step 2: Now divide 403 by 13 to get 31. Step 3: 31 is already the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1209 is: 3 × 13 × 31.
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 1209: (1, 1209), (3, 403), (13, 93), and (31, 39).
Negative factor pairs of 1209: (-1, -1209), (-3, -403), (-13, -93), and (-31, -39).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 93 students and 1209 candies. How will they divide them equally?
They will get 13 candies each.
To divide the candies equally, we need to divide the total candies by the number of students.
1209/93 = 13
A garden is rectangular, the length of the garden is 39 meters and the total area is 1209 square meters. Find the width?
31 meters.
To find the width of the garden, we use the formula, Area = length × width
1209 = 39 × width
To find the value of the width, we need to shift 39 to the left side.
1209/39 = width
Width = 31.
There are 13 buses and 1209 passengers. How many passengers will be in each bus?
Each bus will have 93 passengers.
To find the passengers in each bus, divide the total passengers by the buses.
1209/13 = 93
In an auditorium, there are 1209 seats, and 31 rows. How many seats are there in each row?
There are 39 seats in each row.
Dividing the seats by the total rows, we will get the number of seats in each row.
1209/31 = 39
1209 books need to be arranged in 3 sections. How many books will go in each section?
Each of the sections has 403 books.
Divide total books by sections.
1209/3 = 403
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.
: She loves to read number jokes and games.