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Last updated on May 26th, 2025

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Factors of 1500

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A factor is a number that divides another number evenly without any remainder. We use factors for arranging items or dividing quantities evenly. Let’s learn and see what are the factors of 1500.

Factors of 1500 for Australian Students
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What are the Factors of 1500?

Every number greater than 1 will have a minimum of 2 factors. 


Factors of 1500: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, and 1500.


Negative factors of 1500: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -25, -30, -50, -60, -75, -100, -125, -150, -250, -300, -375, -500, -750, and -1500.


Prime factorization of 1500: 22×53×3


Sum of factors of 1500: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 25 + 30 + 50 + 60 + 75 + 100 + 125 + 150 + 250 + 300 + 375 + 500 + 750 + 1500 = 4368.
 

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How to Find the Factors of 1500?

The methods mentioned below can be used to find the factors of 1500. Use any factor-finding method that is easy for you. 

 

  1. Multiplication method 
  2. Division method 
  3. Prime factorization and prime factors method
  4. Factor tree method
Professor Greenline from BrightChamps

Finding Factors Using Multiplication

Steps:

 

  • Find the pair of numbers which when multiplied gives 1500.

 

  • 1500 is a composite number because it has more than 2 factors.

 

  • The factor pairs of 1500 are:

Positive factor pairs — (1,1500) (2,750) (3,500) (4,375) (5,300) (6,250) (10,150) (12,125) (15,100) (20,75) (25,60) (30,50)


Negative factor pairs — (-1,-1500) (-2,-750) (-3,-500) (-4,-375) (-5,-300) (-6,-250) (-10,-150) (-12,-125) (-15,-100) (-20,-75) (-25,-60) (-30,-50)

Professor Greenline from BrightChamps

Finding Factors by Division Method

Steps: 

  1. Start dividing 1500 with small numbers and check the remainder.
  2. Dividend = Divisor x Quotient + Remainder
  3. The factors of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500. Negative factors are -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -25, -30, -50, -60, -75, -100, -125, -150, -250, -300, -375, -500, -750, and -1500.
Professor Greenline from BrightChamps

Prime Factors and Prime Factorization

Prime factors of 1500: 2, 3, and 5. 


Prime factorization of 1500: 1500 = 2 × 2 × 3 × 5 × 5 × 5


Positive factors of 1500 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, and 1500. 


Negative factors are: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -25, -30, -50, -60, -75, -100, -125, -150, -250, -300, -375, -500, -750, and -1500.

Professor Greenline from BrightChamps

Factor Tree

Factor tree is a graphical representation of breaking down any number into prime factors.


In case of 1500, 


Step 1: First, we write the number on top (in this case, 1500). From there, it will be broken down into 2 parts.
Step 2: Fill in the factor pairs of 1500 in separate steps. In this step, the number will be factorized into 2 and 750.
Step 3: In this step, 750 will again be factorized into 375 and 2. Then it will be factorized down to 375 and 2. We will do the same for 375 and split it into 5 and 75.
Step 4: We will do the same for 75 and break it down into 5 and 15. We can split 15 also into its prime factors, they are 3 and 5.
Step 5: From this, we can find that the prime factors of 1500 are 2, 3, and 5. This is how the factor tree helps to visualize the factors easily to students.
 

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Factor Pairs

Factor pairs are a combination of two numbers, a and b, whose product is equal to 1500. So, over here, a and b are a factor pair of 1500.


The factor pairs of 1500 are


Positive factor pairs:(1,1500), (2,750), (3,500), (4,375), (5,300), (6,250), (10,150), (12,125), (15,100), (20,75), (25,60), (30,50)


Negative factor pairs : (-1,-1500), (-2,-750), (-3,-500), (-4,-375), (-5,-300), (-6,-250), (-10,-150), (-12,-125), (-15,-100), (-20,-75), (-25,-60), (-30,-50)

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in Factors of 1500

It can get really tricky when trying to learn factors, and there is nothing to worry about. We will now take a look at some common mistakes made by students when learning factors. 
 

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Students Can Think Factors Can Only be Small Numbers
 

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

To check factors for any number, it is suggested to start checking with the smallest prime numbers. In many cases, students may get confused that a number can not be factorized further. So it is always good to remember the multiples of few numbers.
 

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Factors of 1500 Examples

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Problem 1

What is the GCF of 1500 and 900?

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Prime factorization:


1500 = 22 × 3 × 53


900 = 22 × 32 × 52


Common factors: 22, 3, and 52


GCF = 22 × 3 × 52 = 4 × 3 × 25 = 300
 

Explanation

The GCF is the largest number that divides both 1500 and 900. 
 

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Problem 2

Is 25 a factor of 1500?

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Divide 1500 ÷ 25 = 60, which is a whole number.


Therefore, 25 is a factor of 1500.
 

Explanation

A number is a factor if it divides evenly by 1500 with no remainder. Since 1500 ÷ 25 = 60, 25 is a factor

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Problem 3

What is the product of the smallest and largest factor of 1500?

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Smallest factor = 1


Largest factor = 1500


Product = 1 × 1500 = 1500
 

Explanation

The smallest factor of any number is 1, and the largest is the number itself. Multiplying these always gives the original number.
 

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FAQs on Factors of 1500

1.What are the even factors of 1500?

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2.Is 1500 a perfect cube?

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3. What are the perfect squares between which 1500 falls?

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4.What do we add to 1500 to make it a perfect square?

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5.How to write 1500 in words?

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6.How can children in Australia use numbers in everyday life to understand Factors of 1500 ?

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7.What are some fun ways kids in Australia can practice Factors of 1500 with numbers?

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8.What role do numbers and Factors of 1500 play in helping children in Australia develop problem-solving skills?

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9.How can families in Australia create number-rich environments to improve Factors of 1500 skills?

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Professor Greenline from BrightChamps

Important Glossaries for Factors of 1500

  • Factors: The numbers which multiplied with each other to get the required numbers are called factors of that number. Example: Factors of 12 are:1 × 12 = 12, 2 × 6 = 12, 3 × 4 = 12. Here, 1, 2, 6, 3, 4 and 12 are the factors of 12.

 

  • Greatest Common Factor (GCF): The greatest number that divides the given number exactly and is a common factor for the given number is called GCF. An example for GCF is: The GCF of 1500, 10, and 100 is 10. Because it is the greatest factor that is common for all three numbers.

 

  • Prime number: Any number greater than 1 and has only 2 factors is called a prime number. Example: 811/1 = 811 and 811/811 = 1. We can see that 811 can be divided exactly by only 2 numbers. Those two numbers are 1 and 811.

 

  • Divisor: Any number that divides another number exactly and leaves no remainder is called a divisor. When we divide 12 by 3, we get a quotient of 4. Here, the divisor is 3 and the dividend is 12.
     
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About BrightChamps in Australia

At BrightChamps, numbers mean more than just digits—they open doors to a world of possibilities! We’re here to help children across Australia grasp essential math skills, focusing today on Factors of 1500 with a special emphasis on factors—in a way that’s fun, engaging, and easy to follow. Whether your child is figuring out the speed of a roller coaster at Luna Park Sydney, keeping score at a local cricket match, or managing their allowance to buy gadgets, understanding numbers builds everyday confidence. Our hands-on lessons make learning enjoyable and straightforward. Since kids in Australia learn differently, we customize lessons to suit each child’s style. From Sydney’s vibrant streets to the beautiful Gold Coast beaches, BrightChamps brings math to life throughout Australia. Let’s make factors an exciting part of every child’s math journey!
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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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Fun Fact

: She loves to read number jokes and games.

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