100 LearnersLast updated on May 26th, 2025
Factors of 10010
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 10010, how they are used in real life, and tips to learn them quickly.
What are the Factors of 10010?
The numbers that divide 10010 evenly are known as factors of 10010.
A factor of 10010 is a number that divides the number without remainder.
The factors of 10010 include 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490, 143, 4905, and 10010.
Negative factors of 10010: -1, -2, -5, -7, -10, -14, -35, -49, -70, -98, -245, -490, -143, -4905, and -10010.
Prime factors of 10010: 2, 5, and 7.
Prime factorization of 10010: 2 × 5 × 7 × 143.
The sum of factors of 10010: 1 + 2 + 5 + 7 + 10 + 14 + 35 + 49 + 70 + 98 + 245 + 490 + 143 + 4905 + 10010 = 15784
How to Find Factors of 10010?
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 10010. Identifying the numbers which are multiplied to get the number 10010 is the multiplication method.
Step 1: Multiply 10010 by 1, 10010 × 1 = 10010.
Step 2: Check for other numbers that give 10010 after multiplying:
2 × 5005 = 10010
5 × 2002 = 10010
7 × 1430 = 10010
10 × 1001 = 10010
Therefore, the positive factor pairs of 10010 are: (1, 10010), (2, 5005), (5, 2002), (7, 1430), and (10, 1001).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 10010 by 1, 10010 ÷ 1 = 10010.
Step 2: Continue dividing 10010 by the numbers until the remainder becomes 0.
10010 ÷ 1 = 10010
10010 ÷ 2 = 5005
10010 ÷ 5 = 2002
10010 ÷ 7 = 1430
10010 ÷ 10 = 1001
Therefore, the factors of 10010 are: 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490, 143, 4905, and 10010.
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 10010 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
10010 ÷ 2 = 5005
5005 ÷ 5 = 1001
1001 ÷ 7 = 143
143 ÷ 11 = 13
13 ÷ 13 = 1
The prime factors of 10010 are 2, 5, 7, 11, and 13.
The prime factorization of 10010 is: 2 × 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, 10010 is divided by 2 to get 5005.
Step 2: Now divide 5005 by 5 to get 1001.
Step 3: Then divide 1001 by 7 to get 143.
Step 4: Divide 143 by 11 to get 13.
Here, 13 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 10010 is: 2 × 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 10010: (1, 10010), (2, 5005), (5, 2002), (7, 1430), and (10, 1001).
Negative factor pairs of 10010: (-1, -10010), (-2, -5005), (-5, -2002), (-7, -1430), and (-10, -1001).
Common Mistakes and How to Avoid Them in Factors of 10010
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 10010, 1 and 10010 are also factors.
Factors of 10010 Examples
Problem 1
There are 10010 marbles and 10 boxes. How will they divide it equally?
They will get 1001 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of boxes.
10010/10 = 1001
Problem 2
A rectangular garden has a length of 7 meters and a total area of 10010 square meters. Find the width.
1430 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
10010 = 7 × width
To find the value of width, we need to shift 7 to the left side.
10010/7 = width
Width = 1430.
Problem 3
There are 4905 candies and 5 jars. How many candies will be in each jar?
Each jar will have 981 candies.
Explanation
To find the candies in each jar, divide the total candies by the jars.
4905/5 = 981
Problem 4
In a school, there are 10010 students, and 2 houses. How many students are there in each house?
There are 5005 students in each house.
Explanation
Dividing the students by the total houses, we will get the number of students in each house.
10010/2 = 5005
Problem 5
10010 pages need to be distributed in 5 different printers. How many pages will each printer get?
Each printer will have 2002 pages.
Explanation
Divide total pages by printers.
10010/5 = 2002
FAQs on Factors of 10010
1.What are the factors of 10010?
2.Mention the prime factors of 10010.
3.Is 10010 a multiple of 7?
4.Mention the factor pairs of 10010?
5.What is the square of 10010?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 10010?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 10010 with numbers?
8.What role do numbers and Factors of 10010 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 10010 skills?
Important Glossaries for Factor of 10010
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 10010 are 1, 2, 5, 7, 10, 14, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 5, 7, 11, and 13 are the prime factors of 10010.
- 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 10010 are (1, 10010), (2, 5005), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, 10010 = 2 × 5 × 7 × 11 × 13.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 10010 is a multiple of 7.
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About BrightChamps in United Arab Emirates
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.
