243 LearnersLast updated on May 26th, 2025
Factors of 1500
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.
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.
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.
- Multiplication method
- Division method
- Prime factorization and prime factors method
- Factor tree method
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)
Finding Factors by Division Method
Steps:
- Start dividing 1500 with small numbers and check the remainder.
- Dividend = Divisor x Quotient + Remainder
- 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.
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.
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.
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)
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
Students Can Think Factors Can Only be Small Numbers
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.
Factors of 1500 Examples
Problem 1
What is the GCF of 1500 and 900?
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.
Problem 2
Is 25 a factor of 1500?
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
Problem 3
What is the product of the smallest and largest factor of 1500?
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.
FAQs on Factors of 1500
1.What are the even factors of 1500?
2.Is 1500 a perfect cube?
3. What are the perfect squares between which 1500 falls?
4.What do we add to 1500 to make it a perfect square?
5.How to write 1500 in words?
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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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.
