129 LearnersLast updated on May 26th, 2025
Factors of 6000
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 6000, how they are used in real life, and tips to learn them quickly.
What are the Factors of 6000?
The numbers that divide 6000 evenly are known as factors of 6000.
A factor of 6000 is a number that divides the number without remainder.
The factors of 6000 include 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000, and 6000.
Negative factors of 6000: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -25, -30, -40, -48, -50, -60, -75, -80, -100, -120, -125, -150, -200, -240, -250, -300, -375, -400, -500, -600, -750, -1000, -1200, -1500, -2000, -3000, and -6000.
Prime factors of 6000: 2, 3, and 5.
Prime factorization of 6000: 24 × 3 × 53.
The sum of factors of 6000: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 25 + 30 + 40 + 48 + 50 + 60 + 75 + 80 + 100 + 120 + 125 + 150 + 200 + 240 + 250 + 300 + 375 + 400 + 500 + 600 + 750 + 1000 + 1200 + 1500 + 2000 + 3000 + 6000 = 22176
How to Find Factors of 6000?
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 multiply to give 6000. Identifying the numbers that are multiplied to get the number 6000 is the multiplication method.
Step 1: Multiply 6000 by 1, 6000 × 1 = 6000.
Step 2: Check for other numbers that give 6000 after multiplying:
2 × 3000 = 6000
3 × 2000 = 6000
4 × 1500 = 6000
5 × 1200 = 6000
6 × 1000 = 6000
8 × 750 = 6000
10 × 600 = 6000
12 × 500 = 6000
15 × 400 = 6000
16 × 375 = 6000
20 × 300 = 6000
24 × 250 = 6000
25 × 240 = 6000
30 × 200 = 6000
40 × 150 = 6000
48 × 125 = 6000
50 × 120 = 6000
60 × 100 = 6000
75 × 80 = 6000
Therefore, the positive factor pairs of 6000 are: (1, 6000), (2, 3000), (3, 2000), (4, 1500), (5, 1200), (6, 1000), (8, 750), (10, 600), (12, 500), (15, 400), (16, 375), (20, 300), (24, 250), (25, 240), (30, 200), (40, 150), (48, 125), (50, 120), (60, 100), (75, 80).
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 6000 by 1, 6000 ÷ 1 = 6000.
Step 2: Continue dividing 6000 by the numbers until the remainder becomes 0.
6000 ÷ 1 = 6000
6000 ÷ 2 = 3000
6000 ÷ 3 = 2000
6000 ÷ 4 = 1500
6000 ÷ 5 = 1200
6000 ÷ 6 = 1000
6000 ÷ 8 = 750
6000 ÷ 10 = 600
6000 ÷ 12 = 500
6000 ÷ 15 = 400
6000 ÷ 16 = 375
6000 ÷ 20 = 300
6000 ÷ 24 = 250
6000 ÷ 25 = 240
6000 ÷ 30 = 200
6000 ÷ 40 = 150
6000 ÷ 48 = 125
6000 ÷ 50 = 120
6000 ÷ 60 = 100
6000 ÷ 75 = 80
Therefore, the factors of 6000 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000, 6000.
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 6000 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
6000 ÷ 2 = 3000
3000 ÷ 2 = 1500
1500 ÷ 2 = 750
750 ÷ 2 = 375
375 ÷ 3 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 6000 are 2, 3, and 5.
The prime factorization of 6000 is: 24 × 3 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 6000 is divided by 2 to get 3000.
Step 2: Now divide 3000 by 2 to get 1500.
Step 3: Then divide 1500 by 2 to get 750.
Step 4: Divide 750 by 2 to get 375.
Step 5: Divide 375 by 3 to get 125.
Step 6: Divide 125 by 5 to get 25.
Step 7: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 6000 is: 24 × 3 × 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 6000: (1, 6000), (2, 3000), (3, 2000), (4, 1500), (5, 1200), (6, 1000), (8, 750), (10, 600), (12, 500), (15, 400), (16, 375), (20, 300), (24, 250), (25, 240), (30, 200), (40, 150), (48, 125), (50, 120), (60, 100), (75, 80).
Negative factor pairs of 6000: (-1, -6000), (-2, -3000), (-3, -2000), (-4, -1500), (-5, -1200), (-6, -1000), (-8, -750), (-10, -600), (-12, -500), (-15, -400), (-16, -375), (-20, -300), (-24, -250), (-25, -240), (-30, -200), (-40, -150), (-48, -125), (-50, -120), (-60, -100), (-75, -80).
Common Mistakes and How to Avoid Them in Factors of 6000
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 6000, 1 and 6000 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 6000 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 6000/1.5 = 4000, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only primes.
For example, thinking all the factors of 6000 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 6000, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing the wrong factors.
For example, not breaking 6000 as 24 × 3 × 53 and missing all the key factors.
Factors of 6000 Examples
Problem 1
There are 6 employees in a company and 6000 files. How will they distribute the files equally?
They will get 1000 files each.
Explanation
To distribute the files equally, we need to divide the total files by the number of employees.
6000/6 = 1000
Problem 2
A garden has a rectangular area, the length of the garden is 150 meters, and the total area is 6000 square meters. Find the width?
40 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
6000 = 150 × width
To find the value of width, we need to shift 150 to the left side.
6000/150 = width
Width = 40.
Problem 3
There are 12 boxes and 6000 marbles. How many marbles will be in each box?
Each box will have 500 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the boxes.
6000/12 = 500
Problem 4
In a concert, there are 6000 attendees, and they are divided into 60 sections. How many attendees are there in each section?
There are 100 attendees in each section.
Explanation
Dividing the attendees by the total sections, we will get the number of attendees in each section.
6000/60 = 100
Problem 5
6000 chairs need to be arranged in 150 rows. How many chairs will go in each row?
Each row will have 40 chairs.
Explanation
Divide the total chairs by the number of rows.
6000/150 = 40
FAQs on Factors of 6000
1.What are the factors of 6000?
2.Mention the prime factors of 6000.
3.Is 6000 a multiple of 4?
4.Mention the factor pairs of 6000?
5.What is the square of 6000?
6.How can children in India use numbers in everyday life to understand Factors of 6000?
7.What are some fun ways kids in India can practice Factors of 6000 with numbers?
8.What role do numbers and Factors of 6000 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 6000 skills?
Important Glossaries for Factors of 6000
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 6000 are 1, 2, 3, 4, 5, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 6000.
- 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 6000 are (1, 6000), (2, 3000), etc.
- Prime factorization: A method of expressing a number as the product of its prime factors. For example, the prime factorization of 6000 is 24 × 3 × 53.
- Multiples: Numbers that can be divided by a given number without leaving a remainder. For example, 6000 is a multiple of 2, 3, and 5.
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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
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