138 LearnersLast updated on May 30th, 2025
Factors of 1215
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.
What are the Factors of 1215?
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
How to Find Factors of 1215?
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 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.
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 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.
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 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.
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of 1215
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 1215, 1 and 1215 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 1215 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 2.5 as a factor because 1215/2.5 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 1215 are prime numbers. For example, 3 and 5 are the prime factors of 1215, but it has other factors like 9, 81.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1215 as 35 × 5 and missing all the key factors.
Factors of 1215 Examples
Problem 1
A community garden has 1215 plants and 15 rows. How many plants are in each row?
There are 81 plants in each row.
Explanation
To divide the plants equally among the rows, divide the total plants by the number of rows.
1215/15 = 81
Problem 2
A stadium has 1215 seats and 27 sections. How many seats are in each section?
45 seats.
Explanation
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
Problem 3
There are 405 marbles and 9 containers. How many marbles will be in each container?
Each container will have 45 marbles.
Explanation
To find the marbles in each container, divide the total marbles by the number of containers.
405/9 = 45
Problem 4
A library has 1215 books and 5 shelves. How many books are on each shelf?
There are 243 books on each shelf.
Explanation
Dividing the books by the number of shelves gives the number of books on each shelf.
1215/5 = 243
Problem 5
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.
Explanation
Divide the total number of students by the number of groups.
1215/81 = 15
FAQs on Factors of 1215
1.What are the factors of 1215?
2.Mention the prime factors of 1215.
3.Is 1215 a multiple of 9?
4.Mention the factor pairs of 1215.
5.What is the square of 1215?
6.How can children in United States use numbers in everyday life to understand Factors of 1215?
7.What are some fun ways kids in United States can practice Factors of 1215 with numbers?
8.What role do numbers and Factors of 1215 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1215 skills?
Important Glossaries for Factor of 1215
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1215 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, and 1215.
- Prime factors: The factors which are prime numbers. For example, 3 and 5 are prime factors of 1215.
- 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 1215 are (1, 1215), (3, 405), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For 1215, it is 35 × 5.
- Multiple: A number that can be divided by another number without a remainder. For example, 1215 is a multiple of 9.
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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.
