What is the Greatest Common Factor of 1500 and 1519?

Greatest common factor (GCF) of 1500 and 1519 is 1.

GCF(1500,1519) = 1

We will now calculate the prime factors of 1500 and 1519, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1500 and 1519.

How to find the GCF of 1500 and 1519?

We will first find the prime factorization of 1500 and 1519. After we will calculate the factors of 1500 and 1519 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 1519

Prime factors of 1519 are 7, 31. Prime factorization of 1519 in exponential form is:

1519 = 7² × 31¹

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 1519

List of positive integer factors of 1519 that divides 1500 without a remainder.

1, 7, 31, 49, 217

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1500 and 1519. The biggest common factor number is the GCF number.
So the greatest common factor 1500 and 1519 is 1.

Also check out the Least Common Multiple of 1500 and 1519