121 LearnersLast updated on May 26th, 2025
Factors of 3675
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 3675, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3675?
The numbers that divide 3675 evenly are known as factors of 3675.
A factor of 3675 is a number that divides the number without remainder.
The positive factors of 3675 are 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, and 3675.
Negative factors of 3675: -1, -3, -5, -7, -15, -21, -25, -35, -49, -75, -105, -147, -175, -245, -525, -735, -1225, and -3675.
Prime factors of 3675: 3, 5, and 7.
Prime factorization of 3675: 3 × 52 × 72.
The sum of factors of 3675: 1 + 3 + 5 + 7 + 15 + 21 + 25 + 35 + 49 + 75 + 105 + 147 + 175 + 245 + 525 + 735 + 1225 + 3675 = 6109
How to Find Factors of 3675?
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 3675. Identifying the numbers which are multiplied to get the number 3675 is the multiplication method.
Step 1: Multiply 3675 by 1, 3675 × 1 = 3675.
Step 2: Check for other numbers that give 3675 after multiplying
3 × 1225 = 3675
5 × 735 = 3675
7 × 525 = 3675
15 × 245 = 3675
21 × 175 = 3675
25 × 147 = 3675
35 × 105 = 3675
49 × 75 = 3675
Therefore, the positive factor pairs of 3675 are: (1, 3675), (3, 1225), (5, 735), (7, 525), (15, 245), (21, 175), (25, 147), (35, 105), (49, 75). 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 3675 by 1, 3675 ÷ 1 = 3675.
Step 2: Continue dividing 3675 by the numbers until the remainder becomes 0.
3675 ÷ 1 = 3675
3675 ÷ 3 = 1225
3675 ÷ 5 = 735
3675 ÷ 7 = 525
3675 ÷ 15 = 245
3675 ÷ 21 = 175
3675 ÷ 25 = 147
3675 ÷ 35 = 105
3675 ÷ 49 = 75
Therefore, the factors of 3675 are: 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, 3675.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 3675 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3675 ÷ 3 = 1225
1225 ÷ 5 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 3675 are 3, 5, and 7.
The prime factorization of 3675 is: 3 × 5^2 × 7^2.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3675 is divided by 3 to get 1225.
Step 2: Now divide 1225 by 5 to get 245.
Step 3: Then divide 245 by 5 to get 49.
Step 4: Divide 49 by 7 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 3675 is: 3 × 52 × 72.
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 3675: (1, 3675), (3, 1225), (5, 735), (7, 525), (15, 245), (21, 175), (25, 147), (35, 105), (49, 75).
Negative factor pairs of 3675: (-1, -3675), (-3, -1225), (-5, -735), (-7, -525), (-15, -245), (-21, -175), (-25, -147), (-35, -105), (-49, -75).
Common Mistakes and How to Avoid Them in Factors of 3675
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 3675, 1 and 3675 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 3675 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 3675/1.5 = 2450, and it 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 3675 are prime numbers.
For example, 3, 5, and 7 are the prime factors of 3675, but it has other factors like 21, 105.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 3675 as 3 × 5^2 × 7^2 and missing all the key factors.
Factors of 3675 Examples
Problem 1
There are 15 participants and 3675 candies. How will they divide it equally?
They will get 245 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of participants.
3675/15 = 245
Problem 2
A garden is rectangular, the length of the garden is 35 meters and the total area is 3675 square meters. Find the width?
105 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
3675 = 35 × width
To find the value of width, we need to shift 35 to the left side.
3675/35 = width
Width = 105.
Problem 3
There are 49 tables and 3675 chairs. How many chairs will be at each table?
Each table will have 75 chairs.
Explanation
To find the chairs at each table, divide the total chairs by the tables.
3675/49 = 75
Problem 4
In an event, there are 3675 attendees, and 25 sections. How many attendees are there in each section?
There are 147 attendees in each section.
Explanation
Dividing the attendees by the total sections, we will get the number of attendees in each section.
3675/25 = 147
Problem 5
3675 books need to be arranged in 21 shelves. How many books will go on each shelf?
Each of the shelves has 175 books.
Explanation
Divide total books by shelves.
3675/21 = 175
FAQs on Factors of 3675
1.What are the factors of 3675?
2.Mention the prime factors of 3675.
3.Is 3675 a multiple of 49?
4.Mention the factor pairs of 3675?
5.What is the square of 3675?
Important Glossaries for Factor of 3675
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3675 are 1, 3, 5, 7, 15, 21, etc.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 7 are prime factors of 3675.
- 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 3675 are (1, 3675), (3, 1225), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 3675 is 3 × 52 × 72.
- Multiple: A number that can be divided by another number without a remainder. For example, 3675 is a multiple of 49.
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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.
