What is the Greatest Common Factor of 19500 and 19506?

Greatest common factor (GCF) of 19500 and 19506 is 6.

GCF(19500,19506) = 6

We will now calculate the prime factors of 19500 and 19506, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19500 and 19506.

How to find the GCF of 19500 and 19506?

We will first find the prime factorization of 19500 and 19506. After we will calculate the factors of 19500 and 19506 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 19506

Prime factors of 19506 are 2, 3, 3251. Prime factorization of 19506 in exponential form is:

19506 = 2¹ × 3¹ × 3251¹

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 19506

List of positive integer factors of 19506 that divides 19500 without a remainder.

1, 2, 3, 6, 3251, 6502, 9753

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19500 and 19506. The biggest common factor number is the GCF number.
So the greatest common factor 19500 and 19506 is 6.

Also check out the Least Common Multiple of 19500 and 19506