What is the Greatest Common Factor of 19500 and 19520?

Greatest common factor (GCF) of 19500 and 19520 is 20.

GCF(19500,19520) = 20

We will now calculate the prime factors of 19500 and 19520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19500 and 19520.

How to find the GCF of 19500 and 19520?

We will first find the prime factorization of 19500 and 19520. After we will calculate the factors of 19500 and 19520 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 19520

Prime factors of 19520 are 2, 5, 61. Prime factorization of 19520 in exponential form is:

19520 = 2⁶ × 5¹ × 61¹

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 19520

List of positive integer factors of 19520 that divides 19500 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 61, 64, 80, 122, 160, 244, 305, 320, 488, 610, 976, 1220, 1952, 2440, 3904, 4880, 9760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19500 and 19520. The biggest common factor number is the GCF number.
So the greatest common factor 19500 and 19520 is 20.

Also check out the Least Common Multiple of 19500 and 19520