Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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: 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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 15 participants and 3675 candies. How will they divide it equally?
They will get 245 candies each.
To divide the candies equally, we need to divide the total candies by the number of participants.
3675/15 = 245
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.
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.
There are 49 tables and 3675 chairs. How many chairs will be at each table?
Each table will have 75 chairs.
To find the chairs at each table, divide the total chairs by the tables.
3675/49 = 75
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.
Dividing the attendees by the total sections, we will get the number of attendees in each section.
3675/25 = 147
3675 books need to be arranged in 21 shelves. How many books will go on each shelf?
Each of the shelves has 175 books.
Divide total books by shelves.
3675/21 = 175
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.
: She loves to read number jokes and games.