100 LearnersLast updated on May 26th, 2025
Factors of 945
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 945, how they are used in real life, and tips to learn them quickly.
What are the Factors of 945?
The numbers that divide 945 evenly are known as factors of 945.
A factor of 945 is a number that divides the number without remainder.
The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, and 945.
Negative factors of 945: -1, -3, -5, -7, -9, -15, -21, -27, -35, -45, -63, -105, -135, -189, -315, and -945.
Prime factors of 945: 3, 5, and 7.
Prime factorization of 945: 3³ × 5 × 7.
The sum of factors of 945: 1 + 3 + 5 + 7 + 9 + 15 + 21 + 27 + 35 + 45 + 63 + 105 + 135 + 189 + 315 + 945 = 2340
How to Find Factors of 945?
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 945. Identifying the numbers which are multiplied to get the number 945 is the multiplication method.
Step 1: Multiply 945 by 1, 945 × 1 = 945.
Step 2: Check for other numbers that give 945 after multiplying
3 × 315 = 945
5 × 189 = 945
7 × 135 = 945
9 × 105 = 945
15 × 63 = 945
21 × 45 = 945
27 × 35 = 945
Therefore, the positive factor pairs of 945 are: (1, 945), (3, 315), (5, 189), (7, 135), (9, 105), (15, 63), (21, 45), and (27, 35).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number by 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 945 by 1, 945 ÷ 1 = 945.
Step 2: Continue dividing 945 by the numbers until the remainder becomes 0.
945 ÷ 1 = 945
945 ÷ 3 = 315
945 ÷ 5 = 189
945 ÷ 7 = 135
945 ÷ 9 = 105
945 ÷ 15 = 63
945 ÷ 21 = 45
945 ÷ 27 = 35
Therefore, the factors of 945 are: 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, and 945.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 945 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
945 ÷ 3 = 315
315 ÷ 3 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 945 are 3, 5, and 7.
The prime factorization of 945 is: 3³ × 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, 945 is divided by 3 to get 315.
Step 2: Now divide 315 by 3 to get 105.
Step 3: Then divide 105 by 3 to get 35.
Step 4: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 945 is: 3³ × 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 945: (1, 945), (3, 315), (5, 189), (7, 135), (9, 105), (15, 63), (21, 45), and (27, 35).
Negative factor pairs of 945: (-1, -945), (-3, -315), (-5, -189), (-7, -135), (-9, -105), (-15, -63), (-21, -45), and (-27, -35).
Common Mistakes and How to Avoid Them in Factors of 945
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 945, 1 and 945 are also factors.
Factors of 945 Examples
Problem 1
There are 9 workers and 945 bricks. How will they divide it equally?
They will get 105 bricks each.
Explanation
To divide the bricks equally, we need to divide the total bricks with the number of workers.
945/9 = 105
Problem 2
A hall is rectangular, the width of the hall is 15 meters and the total area is 945 square meters. Find the length?
63 meters.
Explanation
To find the length of the hall, we use the formula,
Area = length × width
945 = 15 × length
To find the value of length, we need to shift 15 to the left side.
945/15 = length
Length = 63.
Problem 3
There are 27 containers and 945 liters of water. How many liters will be in each container?
Each container will have 35 liters.
Explanation
To find the liters in each container, divide the total liters with the containers.
945/27 = 35
Problem 4
In a school, there are 945 students, and 5 sections. How many students are there in each section?
There are 189 students in each section.
Explanation
Dividing the students with the total sections, we will get the number of students in each section.
945/5 = 189
Problem 5
945 pages need to be arranged in 9 binders. How many pages will go in each binder?
Each of the binders has 105 pages.
Explanation
Divide total pages with binders.
945/9 = 105
FAQs on Factors of 945
1.What are the factors of 945?
2.Mention the prime factors of 945.
3.Is 945 a multiple of 9?
4.Mention the factor pairs of 945?
5.What is the square of 945?
Important Glossaries for Factors of 945
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, and 945.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 7 are prime factors of 945.
- 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 945 are (1, 945), (3, 315), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 945 is 3³ × 5 × 7.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number. For example, finding factor pairs of 945 using multiplication.
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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.
