What is the Greatest Common Factor of 19500 and 19514?

Greatest common factor (GCF) of 19500 and 19514 is 2.

GCF(19500,19514) = 2

We will now calculate the prime factors of 19500 and 19514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19500 and 19514.

How to find the GCF of 19500 and 19514?

We will first find the prime factorization of 19500 and 19514. After we will calculate the factors of 19500 and 19514 and find the biggest common factor number .

Step-1: Prime Factorization of 19500

Prime factors of 19500 are 2, 3, 5, 13. Prime factorization of 19500 in exponential form is:

19500 = 2² × 3¹ × 5³ × 13¹

Step-2: Prime Factorization of 19514

Prime factors of 19514 are 2, 11, 887. Prime factorization of 19514 in exponential form is:

19514 = 2¹ × 11¹ × 887¹

Step-3: Factors of 19500

List of positive integer factors of 19500 that divides 19500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 25, 26, 30, 39, 50, 52, 60, 65, 75, 78, 100, 125, 130, 150, 156, 195, 250, 260, 300, 325, 375, 390, 500, 650, 750, 780, 975, 1300, 1500, 1625, 1950, 3250, 3900, 4875, 6500, 9750

Step-4: Factors of 19514

List of positive integer factors of 19514 that divides 19500 without a remainder.

1, 2, 11, 22, 887, 1774, 9757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19500 and 19514. The biggest common factor number is the GCF number.
So the greatest common factor 19500 and 19514 is 2.

Also check out the Least Common Multiple of 19500 and 19514