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 3645, how they are used in real life, and the tips to learn them quickly.
The numbers that divide 3645 evenly are known as factors of 3645.
A factor of 3645 is a number that divides the number without remainder.
The factors of 3645 include numbers such as 1, 3, 5, 9, 15, 27, 45, 81, 1215, and 3645.
Negative factors of 3645: -1, -3, -5, -9, -15, -27, -45, -81, -1215, and -3645.
Prime factors of 3645: 3 and 5.
Prime factorization of 3645: 34 × 5 × 81.
The sum of factors of 3645: 1 + 3 + 5 + 9 + 15 + 27 + 45 + 81 + 1215 + 3645 = 5046
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 3645. Identifying the numbers which are multiplied to get the number 3645 is the multiplication method.
Step 1: Multiply 3645 by 1, 3645 × 1 = 3645.
Step 2: Check for other numbers that give 3645 after multiplying
3 × 1215 = 3645
5 × 729 = 3645
9 × 405 = 3645
15 × 243 = 3645
27 × 135 = 3645
45 × 81 = 3645
Therefore, the positive factor pairs of 3645 are: (1, 3645), (3, 1215), (5, 729), (9, 405), (15, 243), (27, 135), and (45, 81). 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 3645 by 1, 3645 ÷ 1 = 3645.
Step 2: Continue dividing 3645 by the numbers until the remainder becomes 0.
3645 ÷ 1 = 3645
3645 ÷ 3 = 1215
3645 ÷ 5 = 729
3645 ÷ 9 = 405
3645 ÷ 15 = 243
3645 ÷ 27 = 135
3645 ÷ 45 = 81
Therefore, the factors of 3645 are: 1, 3, 5, 9, 15, 27, 45, 81, 1215, and 3645.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 3645 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3645 ÷ 3 = 1215
1215 ÷ 3 = 405
405 ÷ 3 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of 3645 are 3 and 5.
The prime factorization of 3645 is: 35 × 5.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3645 is divided by 3 to get 1215.
Step 2: Now divide 1215 by 3 to get 405.
Step 3: Then divide 405 by 3 to get 135.
Step 4: Divide 135 by 3 to get 45.
Step 5: Divide 45 by 3 to get 15.
Step 6: Divide 15 by 3 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 3645 is: 35 × 5.
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 3645: (1, 3645), (3, 1215), (5, 729), (9, 405), (15, 243), (27, 135), (45, 81).
Negative factor pairs of 3645: (-1, -3645), (-3, -1215), (-5, -729), (-9, -405), (-15, -243), (-27, -135), (-45, -81).
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 9 friends and 3645 chocolates. How will they divide them equally?
They will get 405 chocolates each.
To divide the chocolates equally, we need to divide the total chocolates by the number of friends.
3645/9 = 405
A field is rectangular, the length of the field is 81 meters, and the total area is 3645 square meters. Find the width.
45 meters.
To find the width of the field, we use the formula,
Area = length × width
3645 = 81 × width
To find the value of width, we need to shift 81 to the left side.
3645/81 = width
Width = 45.
There are 27 bags and 3645 marbles. How many marbles will be in each bag?
Each bag will have 135 marbles.
To find the marbles in each bag, divide the total marbles by the bags.
3645/27 = 135
In a class, there are 3645 students, and 405 groups. How many students are there in each group?
There are 9 students in each group.
Dividing the students by the total groups, we will get the number of students in each group.
3645/405 = 9
3645 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 729 books.
Divide total books by shelves.
3645/5 = 729
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.