What is the Greatest Common Factor of 1500 and 1509?

Greatest common factor (GCF) of 1500 and 1509 is 3.

GCF(1500,1509) = 3

We will now calculate the prime factors of 1500 and 1509, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1500 and 1509.

How to find the GCF of 1500 and 1509?

We will first find the prime factorization of 1500 and 1509. After we will calculate the factors of 1500 and 1509 and find the biggest common factor number .

Step-1: Prime Factorization of 1500

Prime factors of 1500 are 2, 3, 5. Prime factorization of 1500 in exponential form is:

1500 = 2² × 3¹ × 5³

Step-2: Prime Factorization of 1509

Prime factors of 1509 are 3, 503. Prime factorization of 1509 in exponential form is:

1509 = 3¹ × 503¹

Step-3: Factors of 1500

List of positive integer factors of 1500 that divides 1500 without a remainder.

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

Step-4: Factors of 1509

List of positive integer factors of 1509 that divides 1500 without a remainder.

1, 3, 503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1500 and 1509. The biggest common factor number is the GCF number.
So the greatest common factor 1500 and 1509 is 3.

Also check out the Least Common Multiple of 1500 and 1509