127 LearnersLast updated on May 26th, 2025
Factors of 5005
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 5005, how they are used in real life, and tips to learn them quickly.
What are the Factors of 5005?
The numbers that divide 5005 evenly are known as factors of 5005.
A factor of 5005 is a number that divides the number without remainder.
The factors of 5005 are 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 5005.
Negative factors of 5005: -1, -5, -7, -11, -13, -35, -55, -65, -77, -91, -143, -385, -5005.
Prime factors of 5005: 5, 7, 11, and 13.
Prime factorization of 5005: 5 × 7 × 11 × 13.
The sum of factors of 5005: 1 + 5 + 7 + 11 + 13 + 35 + 55 + 65 + 77 + 91 + 143 + 385 + 5005 = 5989
How to Find Factors of 5005?
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 5005. Identifying the numbers which are multiplied to get the number 5005 is the multiplication method.
Step 1: Multiply 5005 by 1, 5005 × 1 = 5005.
Step 2: Check for other numbers that give 5005 after multiplying
5 × 1001 = 5005
7 × 715 = 5005
11 × 455 = 5005
13 × 385 = 5005
35 × 143 = 5005
55 × 91 = 5005
65 × 77 = 5005
Therefore, the positive factor pairs of 5005 are: (1, 5005), (5, 1001), (7, 715), (11, 455), (13, 385), (35, 143), (55, 91), (65, 77).
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 the simple division method
Step 1: Divide 5005 by 1, 5005 ÷ 1 = 5005.
Step 2: Continue dividing 5005 by the numbers until the remainder becomes 0.
5005 ÷ 1 = 5005
5005 ÷ 5 = 1001
5005 ÷ 7 = 715
5005 ÷ 11 = 455
5005 ÷ 13 = 385
5005 ÷ 35 = 143
5005 ÷ 55 = 91
5005 ÷ 65 = 77
Therefore, the factors of 5005 are: 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 5005.
Prime Factors and Prime Factorization
The factors can be found by dividing it with 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 5005 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
5005 ÷ 5 = 1001
1001 ÷ 7 = 143
143 ÷ 11 = 13
13 ÷ 13 = 1
The prime factors of 5005 are 5, 7, 11, and 13.
The prime factorization of 5005 is: 5 × 7 × 11 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 5005 is divided by 5 to get 1001.
Step 2: Now divide 1001 by 7 to get 143. Step 3: Then divide 143 by 11 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 5005 is: 5 × 7 × 11 × 13.
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 5005: (1, 5005), (5, 1001), (7, 715), (11, 455), (13, 385), (35, 143), (55, 91), (65, 77).
Negative factor pairs of 5005: (-1, -5005), (-5, -1001), (-7, -715), (-11, -455), (-13, -385), (-35, -143), (-55, -91), (-65, -77).
Common Mistakes and How to Avoid Them in Factors of 5005
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 word. Always remember to include 1 and the number itself.
For example, in factors of 5005, 1 and 5005 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 5005 consist of -1, -5, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a fraction. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 5005/1.5 = 3336.666..., 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 5005 are prime numbers.
For example, 5, 7, 11, and 13 are the prime factors of 5005, but it has other factors like 35, 65, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 5005 as 5 × 7 × 11 × 13 and missing all the key factors.
Factors of 5005 Examples
Problem 1
A teacher has 5005 pencils and wants to distribute them equally among 5 classes. How many pencils will each class receive?
Each class will receive 1001 pencils.
Explanation
To distribute the pencils equally, we need to divide the total pencils by the number of classes.
5005 ÷ 5 = 1001
Problem 2
A garden is rectangular, the length of the garden is 77 meters, and the total area is 5005 square meters. Find the width.
The width is 65 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
5005 = 77 × width
To find the value of width, we need to shift 77 to the left side.
5005 ÷ 77 = width
Width = 65
Problem 3
There are 143 students and 5005 candies. How many candies will each student get if divided equally?
Each student will get 35 candies.
Explanation
To find the candies each student gets, divide the total candies by the students.
5005 ÷ 143 = 35
Problem 4
A company has 5005 units of product and needs to pack them into 385 boxes. How many units will each box contain?
Each box will contain 13 units.
Explanation
Dividing the units by the total boxes gives the number of units per box.
5005 ÷ 385 = 13
Problem 5
5005 seats need to be arranged in 11 sections in a theater. How many seats will go in each section?
Each section will have 455 seats.
Explanation
Divide the total seats by the sections.
5005 ÷ 11 = 455
FAQs on Factors of 5005
1.What are the factors of 5005?
2.Mention the prime factors of 5005.
3.Is 5005 a multiple of 11?
4.Mention the factor pairs of 5005.
5.What is the square of 5005?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 5005?
7.What are some fun ways kids in United Kingdom can practice Factors of 5005 with numbers?
8.What role do numbers and Factors of 5005 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 5005 skills?
Important Glossaries for Factors of 5005
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 5005 are 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, and 5005.
- Prime factors: The factors which are prime numbers. For example, 5, 7, 11, and 13 are prime factors of 5005.
- 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 5005 are (1, 5005), (5, 1001), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 5005 is 5 × 7 × 11 × 13.
- Multiplication method: A technique used to find factors by identifying pairs of numbers that multiply to give the original number. For example, 5 × 1001 = 5005 is a factor pair of 5005.
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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.
