101 LearnersLast updated on May 27th, 2025
Factors of 675
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 675, how they are used in real life, and tips to learn them quickly.
What are the Factors of 675?
The numbers that divide 675 evenly are known as factors of 675.
A factor of 675 is a number that divides the number without remainder.
The factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, and 675.
Negative factors of 675: -1, -3, -5, -9, -15, -25, -27, -45, -75, -135, -225, and -675.
Prime factors of 675: 3 and 5.
Prime factorization of 675: 33 × 52.
The sum of factors of 675: 1 + 3 + 5 + 9 + 15 + 25 + 27 + 45 + 75 + 135 + 225 + 675 = 1245
How to Find Factors of 675?
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 675. Identifying the numbers which are multiplied to get the number 675 is the multiplication method.
Step 1: Multiply 675 by 1, 675 × 1 = 675.
Step 2: Check for other numbers that give 675 after multiplying
3 × 225 = 675
5 × 135 = 675
9 × 75 = 675
15 × 45 = 675
25 × 27 = 675
Therefore, the positive factor pairs of 675 are: (1, 675), (3, 225), (5, 135), (9, 75), (15, 45), (25, 27). All these factor pairs result in 675. 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 the simple division method
Step 1: Divide 675 by 1, 675 ÷ 1 = 675.
Step 2: Continue dividing 675 by the numbers until the remainder becomes 0.
675 ÷ 1 = 675
675 ÷ 3 = 225
675 ÷ 5 = 135
675 ÷ 9 = 75
675 ÷ 15 = 45
675 ÷ 25 = 27
Therefore, the factors of 675 are: 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675.
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 675 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
675 ÷ 3 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 675 are 3 and 5.
The prime factorization of 675 is: 33 × 52.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 675 is divided by 3 to get 225.
Step 2: Now divide 225 by 3 to get 75.
Step 3: Then divide 75 by 3 to get 25.
Step 4: Divide 25 by 5 to get 5.
Step 5: Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 675 is: 33 × 52.
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 675: (1, 675), (3, 225), (5, 135), (9, 75), (15, 45), (25, 27).
Negative factor pairs of 675: (-1, -675), (-3, -225), (-5, -135), (-9, -75), (-15, -45), (-25, -27).
Common Mistakes and How to Avoid Them in Factors of 675
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 675, 1 and 675 are also factors.
Factors of 675 Examples
Problem 1
There are 9 students and 675 apples. How will they divide it equally?
They will get 75 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of students.
675/9 = 75
Problem 2
A rectangular garden has a length of 15 meters and a total area of 675 square meters. Find the width.
45 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
675 = 15 × width
To find the value of width, we need to shift 15 to the left side.
675/15 = width
Width = 45.
Problem 3
There are 27 boxes and 675 marbles. How many marbles will be in each box?
Each box will have 25 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the boxes.
675/27 = 25
Problem 4
In a conference, there are 225 participants, and 5 breakout rooms. How many participants are there in each room?
There are 45 participants in each room.
Explanation
Dividing the participants by the total rooms, we will get the number of participants in each room.
675/5 = 135
Problem 5
675 books need to be arranged in 15 shelves. How many books will go on each shelf?
Each of the shelves has 45 books.
Explanation
Divide total books by shelves.
675/15 = 45
FAQs on Factors of 675
1.What are the factors of 675?
2.Mention the prime factors of 675.
3.Is 675 a multiple of 9?
4.Mention the factor pairs of 675?
5.What is the square of 675?
6.How can children in Australia use numbers in everyday life to understand Factors of 675?
7.What are some fun ways kids in Australia can practice Factors of 675 with numbers?
8.What role do numbers and Factors of 675 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 675 skills?
Important Glossaries for Factor of 675
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, and 675.
- Prime factors: The factors which are prime numbers. For example, 3 and 5 are prime factors of 675.
- 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 675 are (1, 675), (3, 225), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to a given number.
- Division method: A method to find factors by dividing the number by whole numbers until the remainder is zero.
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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.
