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 1215, how they are used in real life, and tips to learn them quickly.
The numbers that divide 1215 evenly are known as factors of 1215.
A factor of 1215 is a number that divides the number without remainder.
The factors of 1215 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, and 1215.
Negative factors of 1215: -1, -3, -5, -9, -15, -27, -45, -81, -135, -243, -405, and -1215.
Prime factors of 1215: 3 and 5.
Prime factorization of 1215: 35 × 5.
The sum of factors of 1215: 1 + 3 + 5 + 9 + 15 + 27 + 45 + 81 + 135 + 243 + 405 + 1215 = 2184
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 1215. Identifying the numbers which are multiplied to get the number 1215 is the multiplication method.
Step 1: Multiply 1215 by 1, 1215 × 1 = 1215.
Step 2: Check for other numbers that give 1215 after multiplying
3 × 405 = 1215
5 × 243 = 1215
9 × 135 = 1215
15 × 81 = 1215
27 × 45 = 1215
Therefore, the positive factor pairs of 1215 are: (1, 1215), (3, 405), (5, 243), (9, 135), (15, 81), (27, 45). All these factor pairs result in 1215. For every positive factor, there is a negative factor.
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 1215 by 1, 1215 ÷ 1 = 1215.
Step 2: Continue dividing 1215 by the numbers until the remainder becomes 0.
1215 ÷ 1 = 1215
1215 ÷ 3 = 405
1215 ÷ 5 = 243
1215 ÷ 9 = 135
1215 ÷ 15 = 81
1215 ÷ 27 = 45
Therefore, the factors of 1215 are: 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 1215 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1215 ÷ 3 = 405
405 ÷ 3 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of 1215 are 3 and 5.
The prime factorization of 1215 is: 35 × 5.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1215 is divided by 3 to get 405.
Step 2: Now divide 405 by 3 to get 135.
Step 3: Then divide 135 by 3 to get 45.
Step 4: Divide 45 by 3 to get 15.
Step 5: Divide 15 by 3 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1215 is: 35 × 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 1215: (1, 1215), (3, 405), (5, 243), (9, 135), (15, 81), (27, 45).
Negative factor pairs of 1215: (-1, -1215), (-3, -405), (-5, -243), (-9, -135), (-15, -81), (-27, -45).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A community garden has 1215 plants and 15 rows. How many plants are in each row?
There are 81 plants in each row.
To divide the plants equally among the rows, divide the total plants by the number of rows.
1215/15 = 81
A stadium has 1215 seats and 27 sections. How many seats are in each section?
45 seats.
To find the seats in each section, use the formula, Total seats = sections × seats per section
1215 = 27 × seats per section
To find the value of seats per section, divide 1215 by 27.
1215/27 = 45
There are 405 marbles and 9 containers. How many marbles will be in each container?
Each container will have 45 marbles.
To find the marbles in each container, divide the total marbles by the number of containers.
405/9 = 45
A library has 1215 books and 5 shelves. How many books are on each shelf?
There are 243 books on each shelf.
Dividing the books by the number of shelves gives the number of books on each shelf.
1215/5 = 243
A school has 1215 students, and they need to be divided into 81 groups. How many students will be in each group?
Each group will have 15 students.
Divide the total number of students by the number of groups.
1215/81 = 15
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.