Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a 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 1005, how they are used in real life, and tips to learn them quickly.
The numbers that divide 1005 evenly are known as factors of 1005.
A factor of 1005 is a number that divides the number without a remainder.
The factors of 1005 are 1, 3, 5, 15, 67, 201, 335, and 1005.
Negative factors of 1005: -1, -3, -5, -15, -67, -201, -335, and -1005.
Prime factors of 1005: 3, 5, and 67.
Prime factorization of 1005: 3 × 5 × 67.
The sum of factors of 1005: 1 + 3 + 5 + 15 + 67 + 201 + 335 + 1005 = 1632
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 1005. Identifying the numbers which are multiplied to get the number 1005 is the multiplication method.
Step 1: Multiply 1005 by 1, 1005 × 1 = 1005.
Step 2: Check for other numbers that give 1005 after multiplying 3 × 335 = 1005 5 × 201 = 1005 15 × 67 = 1005
Therefore, the positive factor pairs of 1005 are: (1, 1005), (3, 335), (5, 201), (15, 67).
All these factor pairs result in 1005.
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 a whole number as factors. Factors can be calculated by following the simple division method
Step 1: Divide 1005 by 1, 1005 ÷ 1 = 1005.
Step 2: Continue dividing 1005 by the numbers until the remainder becomes 0.
1005 ÷ 1 = 1005
1005 ÷ 3 = 335
1005 ÷ 5 = 201
1005 ÷ 15 = 67
Therefore, the factors of 1005 are: 1, 3, 5, 15, 67, 201, 335, and 1005.
The factors can be found by dividing it with a prime number. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 1005 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
1005 ÷ 3 = 335
335 ÷ 5 = 67
67 ÷ 67 = 1
The prime factors of 1005 are 3, 5, and 67.
The prime factorization of 1005 is: 3 × 5 × 67.
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1005 is divided by 3 to get 335.
Step 2: Now divide 335 by 5 to get 67.
Step 3: Here, 67 is a prime number that cannot be divided anymore. So, the prime factorization of 1005 is: 3 × 5 × 67.
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 1005: (1, 1005), (3, 335), (5, 201), and (15, 67).
Negative factor pairs of 1005: (-1, -1005), (-3, -335), (-5, -201), and (-15, -67).
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 5 friends and 1005 chocolates. How will they divide it equally?
They will get 201 chocolates each.
To divide the chocolates equally, we need to divide the total chocolates by the number of friends.
1005/5 = 201
A field is rectangular, the length of the field is 15 meters and the total area is 1005 square meters. Find the width.
67 meters.
To find the width of the field, we use the formula,
Area = length × width
1005 = 15 × width
To find the value of width, we need to shift 15 to the left side.
1005/15 = width
Width = 67.
There are 67 bags and 1005 candies. How many candies will be in each bag?
Each bag will have 15 candies.
To find the candies in each bag, divide the total candies by the bags.
1005/67 = 15
In a class, there are 1005 students, and 3 groups. How many students are there in each group?
There are 335 students in each group.
Dividing the students by the total groups, we will get the number of students in each group.
1005/3 = 335
1005 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each shelf has 201 books.
Divide total books by shelves.
1005/5 = 201
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.