A day full of math games & activities. Find one near you.

Factors of 1500

Factors of 1500 are the list of integers that can be evenly divided into 1500. There are total 24 factors of 1500, of which 2, 3, 5 are its prime factors. The Prime Factorization of 1500 is 2² × 3¹ × 5³.

All 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 Factors of 1500: 2, 3, 5
Prime Factorization of 1500: 2² × 3¹ × 5³
Sum of Factors of 1500: 4368

1.	What Are the Factors of 1500?
2.	Factors of 1500 by Prime Factorization
3.	Factors of 1500 in Pairs
4.	FAQs on Factors of 1500

What are Factors of 1500?

Factors of 1500 are pairs of those numbers whose products result in 1500. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1500?

To find the factors of 1500, we will have to find the list of numbers that would divide 1500 without leaving any remainder.

1500/300 = 5; therefore, 300 is a factor of 1500 and 5 is also a factor of 1500.
1500/500 = 3; therefore, 500 is a factor of 1500 and 3 is also a factor of 1500.

Similarly we can find other factors. Hence, 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.

☛ Also Check:

Factors of 121 - The factors of 121 are 1, 11, 121
Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98
Factors of 20 - The factors of 20 are 1, 2, 4, 5, 10, 20
Factors of 14 - The factors of 14 are 1, 2, 7, 14
Factors of 25 - The factors of 25 are 1, 5, 25

Factors of 1500 by Prime Factorization

The number 1500 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1500. The first step is to divide the number 1500 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1500 ÷ 2 = 750
750 ÷ 2 = 375

Further dividing 375 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 375 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 1500 can be written as 2² × 3¹ × 5³ where 2, 3, 5 are prime.

Factors of 1500 in Pairs

Pair factors of 1500 are the pairs of numbers that when multiplied give the product 1500. The factors of 1500 in pairs are:

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

Negative pair factors of 1500 are:

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

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 1500 Solved Examples

Example 1: How many factors are there for 1500?

Solution:

The factors of 1500 are too many, therefore if we can find the prime factorization of 1500, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^x × b^y × c^z where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 1500 = 2² × 3¹ × 5³
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (3 + 1) = 3 × 2 × 4 = 24
Example 2: Find the LCM and Greatest Common Factor (GCF) of 1500 and 576.

Solution:

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 and factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576.

Therefore, the LCM of 1500 and 576 is 72000 and Greatest Common Factor (GCF) of 1500 and 576 is 12.
Example 3: Find if 5, 6, 20, 25, 50, 153, 500 and 1500 are factors of 1500.

Solution:

When we divide 1500 by 153 it leaves a remainder. Therefore, the number 153 is not a factor of 1500. All numbers except 153 are factors of 1500.
Example 4: Find the product of all the prime factors of 1500.

Solution:

Since, the prime factors of 1500 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.

go to slide go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

go to slide go to slide go to slide go to slide go to slide

FAQs on Factors of 1500

What are the Factors of 1500?

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 and its 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, -1500.

What is the Sum of all Factors of 1500?

Sum of all factors of 1500 = (2^{2 + 1} - 1)/(2 - 1) × (3^{1 + 1} - 1)/(3 - 1) × (5^{3 + 1} - 1)/(5 - 1) = 4368

What numbers are the Pair Factors of 1500?

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

What is the Greatest Common Factor of 1500 and 1443?

The factors of 1500 and 1443 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 and 1, 3, 13, 37, 39, 111, 481, 1443 respectively.

Common factors of 1500 and 1443 are [1, 3].

Hence, the Greatest Common Factor of 1500 and 1443 is 3.

How Many Factors of 1500 are also common to the Factors of 1213?

Since, 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 and factors of 1213 are 1, 1213. Hence, 1500 and 1213 have only one common factor which is 1. Therefore, 1500 and 1213 are co-prime.

Math worksheets and
visual curriculum