132 LearnersLast updated on May 26th, 2025
Factors of 1000
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 1000, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1000?
The numbers that divide 1000 evenly are known as factors of 1000.
A factor of 1000 is a number that divides the number without remainder.
The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.
Negative factors of 1000: -1, -2, -4, -5, -8, -10, -20, -25, -40, -50, -100, -125, -200, -250, -500, and -1000.
Prime factors of 1000: 2 and 5.
Prime factorization of 1000: (23 × 53).
The sum of factors of 1000: 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 40 + 50 + 100 + 125 + 200 + 250 + 500 + 1000 = 2340
How to Find Factors of 1000?
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 1000. Identifying the numbers which are multiplied to get the number 1000 is the multiplication method.
Step 1: Multiply 1000 by 1, 1000 × 1 = 1000.
Step 2: Check for other numbers that give 1000 after multiplying: (2 × 500 = 1000) (4 × 250 = 1000) (5 × 200 = 1000) (8 × 125 = 1000) (10 × 100 = 1000) (20 × 50 = 1000) (25 × 40 = 1000)
Therefore, the positive factor pairs of 1000 are: (1, 1000), (2, 500), (4, 250), (5, 200), (8, 125), (10, 100), (20, 50), (25, 40).
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 1000 by 1, (1000 div 1 = 1000).
Step 2: Continue dividing 1000 by the numbers until the remainder becomes 0. (1000 div 1 = 1000) \(1000 div 2 = 500) (1000 div 4 = 250) (1000 div 5 = 200) (1000 div 8 = 125) (1000 div 10 = 100)
Therefore, the factors of 1000 are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.
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 1000 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1. (1000 div 2 = 500) (500 div 2 = 250) (250 div 2 = 125) (125 div 5 = 25) (25 div 5 = 5) (5 div 5 = 1)
The prime factors of 1000 are 2 and 5.
The prime factorization of 1000 is: (23 × 53).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 1000 is divided by 2 to get 500.
Step 2: Now divide 500 by 2 to get 250.
Step 3: Then divide 250 by 2 to get 125.
Step 4: Divide 125 by 5 to get 25.
Step 5: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1000 is: (23 × 53).
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 1000: (1, 1000), (2, 500), (4, 250), (5, 200), (8, 125), (10, 100), (20, 50), (25, 40).
Negative factor pairs of 1000: (-1, -1000), (-2, -500), (-4, -250), (-5, -200), (-8, -125), (-10, -100), (-20, -50), (-25, -40).
Common Mistakes and How to Avoid Them in Factors of 1000
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 1000, 1 and 1000 are also factors.
Mistake 2
Missing Negative Factors
We often only mention positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 1000 include -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes mistakenly add fractions as factors. Only whole numbers can be a factor. For example, thinking 1.5 is a factor because (1000 div 1.5 = 666.67), 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 1000 are prime numbers.
For example, 2 and 5 are the prime factors of 1000, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing the wrong factors.
For example, not breaking 1000 as (23 × 53) and missing all the key factors.
Factors of 1000 Examples
Problem 1
There are 10 students and 1000 apples. How will they divide them equally?
They will get 100 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of students.
(1000 div 10 = 100)
Problem 2
A rectangular swimming pool has a length of 20 meters, and the total area is 1000 square meters. Find the width.
50 meters.
Explanation
To find the width of the swimming pool, we use the formula,
Area = length × width
1000 = 20 × width
To find the value of the width, we need to shift 20 to the left side.
1000 div 20 = width
Width = 50.
Problem 3
There are 25 cartons and 1000 candies. How many candies will be in each carton?
Each carton will have 40 candies.
Explanation
To find the candies in each carton, divide the total candies by the cartons.
1000 div 25 = 40
Problem 4
In a company, there are 1000 employees, and 250 teams. How many employees are there in each team?
There are 4 employees in each team.
Explanation
Dividing the employees by the total teams, we will get the number of employees in each team.
1000 div 250 = 4
Problem 5
1000 books need to be arranged in 50 shelves. How many books will go on each shelf?
Each of the shelves has 20 books.
Explanation
Divide total books by shelves.
1000 div 50 = 20
FAQs on Factors of 1000
1.What are the factors of 1000?
2.Mention the prime factors of 1000.
3.Is 1000 a multiple of 4?
4.Mention the factor pairs of 1000.
5.What is the cube of 10?
6.How can children in Thailand use numbers in everyday life to understand Factors of 1000?
7.What are some fun ways kids in Thailand can practice Factors of 1000 with numbers?
8.What role do numbers and Factors of 1000 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 1000 skills?
Important Glossaries for Factor of 1000
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.
- Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of 1000.
- 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 1000 are (1, 1000), (2, 500), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1000 is 23 × 53.
- Multiples: Numbers that are the product of a given number and an integer. For example, 1000 is a multiple of 4.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 1000
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.
