101 LearnersLast updated on May 26th, 2025
Factors of 12000
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 12000, how they are used in real life, and tips to learn them quickly.
What are the Factors of 12000?
The numbers that divide 12000 evenly are known as factors of 12000.
A factor of 12000 is a number that divides the number without remainder.
The factors of 12000 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, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 2400, 3000, 4000, 6000, and 12000.
Negative factors of 12000: -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, -300, -375, -400, -500, -600, -750, -1000, -1200, -1500, -2000, -2400, -3000, -4000, -6000, and -12000.
Prime factors of 12000: 2, 3, and 5.
Prime factorization of 12000: 2^6 × 3 × 5^3.
The sum of factors of 12000: 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 + 300 + 375 + 400 + 500 + 600 + 750 + 1000 + 1200 + 1500 + 2000 + 2400 + 3000 + 4000 + 6000 + 12000 = 42078
How to Find Factors of 12000?
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 12000. Identifying the numbers which are multiplied to get the number 12000 is the multiplication method.
Step 1: Multiply 12000 by 1, 12000 × 1 = 12000.
Step 2: Check for other numbers that give 12000 after multiplying
2 × 6000 = 12000
3 × 4000 = 12000
4 × 3000 = 12000
5 × 2400 = 12000
6 × 2000 = 12000
8 × 1500 = 12000
10 × 1200 = 12000
12 × 1000 = 12000
15 × 800 = 12000
20 × 600 = 12000
24 × 500 = 12000
25 × 480 = 12000
30 × 400 = 12000
40 × 300 = 12000
48 × 250 = 12000
50 × 240 = 12000
60 × 200 = 12000
75 × 160 = 12000
80 × 150 = 12000
100 × 120 = 12000
120 × 100 = 12000
Therefore, the positive factor pairs of 12000 are: (1, 12000), (2, 6000), (3, 4000), (4, 3000), (5, 2400), (6, 2000), (8, 1500), (10, 1200), (12, 1000), (15, 800), (20, 600), (24, 500), (25, 480), (30, 400), (40, 300), (48, 250), (50, 240), (60, 200), (75, 160), (80, 150), (100, 120).
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 in whole numbers as factors. Factors can be calculated by following the simple division method -
Step 1: Divide 12000 by 1, 12000 ÷ 1 = 12000.
Step 2: Continue dividing 12000 by the numbers until the remainder becomes 0.
12000 ÷ 1 = 12000
12000 ÷ 2 = 6000
12000 ÷ 3 = 4000
12000 ÷ 4 = 3000
12000 ÷ 5 = 2400
12000 ÷ 6 = 2000
12000 ÷ 8 = 1500
12000 ÷ 10 = 1200
12000 ÷ 12 = 1000
12000 ÷ 15 = 800
12000 ÷ 20 = 600
12000 ÷ 24 = 500
12000 ÷ 25 = 480
12000 ÷ 30 = 400
12000 ÷ 40 = 300
12000 ÷ 48 = 250
12000 ÷ 50 = 240
12000 ÷ 60 = 200
12000 ÷ 75 = 160
12000 ÷ 80 = 150
12000 ÷ 100 = 120
Therefore, the factors of 12000 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, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 2400, 3000, 4000, 6000, 12000.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 12000 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
12000 ÷ 2 = 6000
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 12000 are 2, 3, and 5.
The prime factorization of 12000 is: 2^6 × 3 × 5^3.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 12000 is divided by 2 to get 6000.
Step 2: Now divide 6000 by 2 to get 3000.
Step 3: Then divide 3000 by 2 to get 1500.
Step 4: Divide 1500 by 2 to get 750.
Step 5: Divide 750 by 2 to get 375.
Step 6: Divide 375 by 3 to get 125.
Step 7: Divide 125 by 5 to get 25.
Step 8: Divide 25 by 5 to get 5.
Here, 5 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 12000 is: 2^6 × 3 × 5^3.
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 12000: (1, 12000), (2, 6000), (3, 4000), (4, 3000), (5, 2400), (6, 2000), (8, 1500), (10, 1200), (12, 1000), (15, 800), (20, 600), (24, 500), (25, 480), (30, 400), (40, 300), (48, 250), (50, 240), (60, 200), (75, 160), (80, 150), (100, 120).
Negative factor pairs of 12000: (-1, -12000), (-2, -6000), (-3, -4000), (-4, -3000), (-5, -2400), (-6, -2000), (-8, -1500), (-10, -1200), (-12, -1000), (-15, -800), (-20, -600), (-24, -500), (-25, -480), (-30, -400), (-40, -300), (-48, -250), (-50, -240), (-60, -200), (-75, -160), (-80, -150), (-100, -120).
Common Mistakes and How to Avoid Them in Factors of 12000
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 12000, 1 and 12000 are also factors.
Factors of 12000 Examples
Problem 1
There are 12 teams and 12000 junior athletes. How will they be divided equally among the teams?
They will get 1000 junior athletes each.
Explanation
To divide the junior athletes equally, we need to divide the total number by the number of teams.
12000/12 = 1000
Problem 2
A large field is rectangular, the length of the field is 150 meters and the total area is 12000 square meters. Find the width?
80 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
12000 = 150 × width
To find the value of the width, we need to shift 150 to the left side.
12000/150 = width
Width = 80.
Problem 3
There are 25 buses and 12000 passengers. How many passengers will be in each bus?
Each bus will have 480 passengers.
Explanation
To find the passengers in each bus, divide the total number of passengers by the number of buses.
12000/25 = 480
Problem 4
In a school, there are 12000 students, and 60 classes. How many students are there in each class?
There are 200 students in each class.
Explanation
Dividing the students by the total number of classes, we will get the number of students in each class.
12000/60 = 200
Problem 5
12000 books need to be arranged in 40 shelves. How many books will go on each shelf?
Each of the shelves has 300 books.
Explanation
Divide the total number of books by the number of shelves.
12000/40 = 300
FAQs on Factors of 12000
1.What are the factors of 12000?
2.Mention the prime factors of 12000.
3.Is 12000 a multiple of 25?
4.Mention the factor pairs of 12000.
5.What is the square of 12000?
6.How can children in Philippines use numbers in everyday life to understand Factors of 12000?
7.What are some fun ways kids in Philippines can practice Factors of 12000 with numbers?
8.What role do numbers and Factors of 12000 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Factors of 12000 skills?
Important Glossaries for Factor of 12000
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 12000 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, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 2400, 3000, 4000, 6000, and 12000.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 12000.
- 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 12000 are (1, 12000), (2, 6000), etc.
- Multiples: Multiples are the numbers that can be divided by a given number without a remainder. For example, 12000 is a multiple of 25.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 12000 is 2^6 × 3 × 5^3.
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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.
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