117 LearnersLast updated on May 26th, 2025
Factors of 1005
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.
What are the Factors of 1005?
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
How to Find Factors of 1005?
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 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.
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 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.
Prime Factors and Prime Factorization
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
- Using factor tree
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.
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of 1005
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 1005, 1 and 1005 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1005 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1005/1.5 = 670, 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 1005 are prime numbers.
For example, 3, 5, and 67 are the prime factors of 1005, but it has other factors like 15, 335.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1005 as 3 × 5 × 67 and missing all the key factors.
Factors of 1005 Examples
Problem 1
There are 5 friends and 1005 chocolates. How will they divide it equally?
They will get 201 chocolates each.
Explanation
To divide the chocolates equally, we need to divide the total chocolates by the number of friends.
1005/5 = 201
Problem 2
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.
Explanation
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.
Problem 3
There are 67 bags and 1005 candies. How many candies will be in each bag?
Each bag will have 15 candies.
Explanation
To find the candies in each bag, divide the total candies by the bags.
1005/67 = 15
Problem 4
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.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1005/3 = 335
Problem 5
1005 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each shelf has 201 books.
Explanation
Divide total books by shelves.
1005/5 = 201
FAQs on Factors of 1005
1.What are the factors of 1005?
2.Mention the prime factors of 1005.
3.Is 1005 a multiple of 5?
4.Mention the factor pairs of 1005.
5.What is the square of 1005?
6.How can children in Thailand use numbers in everyday life to understand Factors of 1005?
7.What are some fun ways kids in Thailand can practice Factors of 1005 with numbers?
8.What role do numbers and Factors of 1005 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 1005 skills?
Important Glossaries for Factor of 1005
- Factors: The numbers that divide a given number without leaving a remainder are called factors. For example, the factors of 1005 are 1, 3, 5, 15, 67, 201, 335, and 1005.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 67 are prime factors of 1005.
- 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 1005 are (1, 1005), (3, 335), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1005 is 3 × 5 × 67.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
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About BrightChamps in Thailand
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.
