104 LearnersLast updated on May 26th, 2025
Factors of 315
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 315, how they are used in real life, and tips to learn them quickly.
What are the Factors of 315?
The numbers that divide 315 evenly are known as factors of 315.
A factor of 315 is a number that divides the number without a remainder.
The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315.
Negative factors of 315: -1, -3, -5, -7, -9, -15, -21, -35, -45, -63, -105, and -315.
Prime factors of 315: 3, 5, and 7.
Prime factorization of 315: 3² × 5 × 7.
The sum of factors of 315: 1 + 3 + 5 + 7 + 9 + 15 + 21 + 35 + 45 + 63 + 105 + 315 = 624
How to Find Factors of 315?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 315. Identifying the numbers which are multiplied to get the number 315 is the multiplication method.
Step 1: Multiply 315 by 1, 315 × 1 = 315.
Step 2: Check for other numbers that give 315 after multiplying
3 × 105 = 315
5 × 63 = 315
7 × 45 = 315
9 × 35 = 315
15 × 21 = 315
Therefore, the positive factor pairs of 315 are: (1, 315), (3, 105), (5, 63), (7, 45), (9, 35), (15, 21).
All these factor pairs result in 315. 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 in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 315 by 1, 315 ÷ 1 = 315.
Step 2: Continue dividing 315 by the numbers until the remainder becomes 0.
315 ÷ 1 = 315
315 ÷ 3 = 105
315 ÷ 5 = 63
315 ÷ 7 = 45
315 ÷ 9 = 35
315 ÷ 15 = 21
Therefore, the factors of 315 are: 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.
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 315 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
315 ÷ 3 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 315 are 3, 5, and 7.
The prime factorization of 315 is: 3² × 5 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 315 is divided by 3 to get 105.
Step 2: Now divide 105 by 3 to get 35.
Step 3: Then divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 315 is: 3² × 5 × 7.
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 315: (1, 315), (3, 105), (5, 63), (7, 45), (9, 35), (15, 21).
Negative factor pairs of 315: (-1, -315), (-3, -105), (-5, -63), (-7, -45), (-9, -35), (-15, -21).
Common Mistakes and How to Avoid Them in Factors of 315
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 word. Always remember to include 1 and the number itself.
For example, in factors of 315, 1 and 315 are also factors.
Factors of 315 Examples
Problem 1
There are 9 baskets and 315 apples. How will they distribute them equally?
They will get 35 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of baskets. 315/9 = 35
Problem 2
A rectangular garden has a length of 5 meters and a total area of 315 square meters. Find the width?
63 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
315 = 5 × width
To find the value of width, we need to shift 5 to the left side.
315/5 = width
Width = 63.
Problem 3
There are 21 boxes and 315 candies. How many candies will be in each box?
Each box will have 15 candies.
Explanation
To find the candies in each box, divide the total candies with the boxes. 315/21 = 15
Problem 4
In a class, there are 315 students, and 15 teams. How many students are in each team?
There are 21 students in each team.
Explanation
Dividing the students with the total teams, we will get the number of students in each team. 315/15 = 21
Problem 5
315 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 105 books.
Explanation
Divide total books with shelves. 315/3 = 105
FAQs on Factors of 315
1.What are the factors of 315?
2.Mention the prime factors of 315.
3.Is 315 a multiple of 9?
4.Mention the factor pairs of 315?
5.What is the square of 315?
6.How can children in Saudi Arabia use numbers in everyday life to understand Factors of 315?
7.What are some fun ways kids in Saudi Arabia can practice Factors of 315 with numbers?
8.What role do numbers and Factors of 315 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Factors of 315 skills?
Important Glossaries for Factor of 315
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 7 are prime factors of 315.
- 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 315 are (1, 315), (3, 105), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For 315, it is 3² × 5 × 7.
- Negative factors: Factors that are negative numbers. For instance, -1, -3, -5, etc., are negative factors of 315.
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About BrightChamps in Saudi Arabia
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.
