What is the Greatest Common Factor of 1500 and 1517?

Greatest common factor (GCF) of 1500 and 1517 is 1.

GCF(1500,1517) = 1

We will now calculate the prime factors of 1500 and 1517, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1500 and 1517.

How to find the GCF of 1500 and 1517?

We will first find the prime factorization of 1500 and 1517. After we will calculate the factors of 1500 and 1517 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 1517

Prime factors of 1517 are 37, 41. Prime factorization of 1517 in exponential form is:

1517 = 37¹ × 41¹

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 1517

List of positive integer factors of 1517 that divides 1500 without a remainder.

1, 37, 41

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1500 and 1517. The biggest common factor number is the GCF number.
So the greatest common factor 1500 and 1517 is 1.

Also check out the Least Common Multiple of 1500 and 1517