Last updated on May 26th, 2025
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 30000, how they are used in real life, and tips to learn them quickly.
The numbers that divide 30000 evenly are known as factors of 30000.
A factor of 30000 is a number that divides the number without remainder.
The factors of 30000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 160, 200, 240, 300, 375, 400, 480, 500, 600, 750, 800, 1000, 1200, 1500, 2000, 2400, 3000, 3750, 4000, 5000, 6000, 7500, 10000, 12000, 15000, and 30000.
Negative factors of 30000: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -25, -30, -40, -48, -50, -60, -75, -80, -100, -120, -150, -160, -200, -240, -300, -375, -400, -480, -500, -600, -750, -800, -1000, -1200, -1500, -2000, -2400, -3000, -3750, -4000, -5000, -6000, -7500, -10000, -12000, -15000, and -30000.
Prime factors of 30000: 2, 3, and 5.
Prime factorization of 30000: 24 × 3 × 54.
The sum of factors of 30000: 93078
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 30000. Identifying the numbers which are multiplied to get the number 30000 is the multiplication method.
Step 1: Multiply 30000 by 1, 30000 × 1 = 30000.
Step 2: Check for other numbers that give 30000 after multiplying:
2 × 15000 = 30000
3 × 10000 = 30000
4 × 7500 = 30000
5 × 6000 = 30000
6 × 5000 = 30000
8 × 3750 = 30000
10 × 3000 = 30000
12 × 2500 = 30000
15 × 2000 = 30000 ... and so on.
Therefore, the positive factor pairs of 30000 are numerous. For every positive factor, there is a negative factor.
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 30000 by 1, 30000 ÷ 1 = 30000.
Step 2: Continue dividing 30000 by the numbers until the remainder becomes 0.
30000 ÷ 1 = 30000
30000 ÷ 2 = 15000
30000 ÷ 3 = 10000
30000 ÷ 4 = 7500
30000 ÷ 5 = 6000 ... and so on.
Therefore, the factors of 30000 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 160, 200, 240, 300, 375, 400, 480, 500, 600, 750, 800, 1000, 1200, 1500, 2000, 2400, 3000, 3750, 4000, 5000, 6000, 7500, 10000, 12000, 15000, and 30000.
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 30000 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
30000 ÷ 2 = 15000
15000 ÷ 2 = 7500
7500 ÷ 2 = 3750
3750 ÷ 2 = 1875
1875 ÷ 3 = 625
625 ÷ 5 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 30000 are 2, 3, and 5.
The prime factorization of 30000 is: 24 × 3 × 54.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 30000 is divided by 2 to get 15000.
Step 2: Now divide 15000 by 2 to get 7500.
Step 3: Then divide 7500 by 2 to get 3750.
Step 4: Divide 3750 by 2 to get 1875.
Step 5: Divide 1875 by 3 to get 625.
Step 6: Divide 625 by 5 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 30000 is: 24 × 3 × 54.
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 30000 include: (1, 30000), (2, 15000), (3, 10000), (4, 7500), and so on.
Negative factor pairs of 30000 include: (-1, -30000), (-2, -15000), (-3, -10000), (-4, -7500), and so on.
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A company has 30000 products and wants to distribute them in 50 stores. How many products will each store receive?
Each store will receive 600 products.
To distribute the products equally, divide the total products by the number of stores.
30000/50 = 600
A rectangular garden has an area of 30000 square meters and a length of 150 meters. What is its width?
200 meters.
To find the width of the garden, we use the formula,
Area = length × width
30000 = 150 × width
To find the value of width, divide 30000 by 150.
30000/150 = width
Width = 200.
A bakery produced 30000 cookies and wants to pack them into boxes of 250 each. How many boxes are needed?
120 boxes are needed.
To find the number of boxes needed, divide the total cookies by the cookies per box.
30000/250 = 120
A company has 30000 flyers to distribute equally among 15 branches. How many flyers will each branch receive?
Each branch will receive 2000 flyers.
Divide the total flyers by the number of branches to get the number of flyers per branch.
30000/15 = 2000
30000 books need to be arranged in 100 shelves. How many books will go on each shelf?
Each shelf will have 300 books.
Divide total books by shelves.
30000/100 = 300
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.
: She loves to read number jokes and games.