What is the Greatest Common Factor of 19491 and 19500?

Greatest common factor (GCF) of 19491 and 19500 is 3.

GCF(19491,19500) = 3

We will now calculate the prime factors of 19491 and 19500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19491 and 19500.

How to find the GCF of 19491 and 19500?

We will first find the prime factorization of 19491 and 19500. After we will calculate the factors of 19491 and 19500 and find the biggest common factor number .

Step-1: Prime Factorization of 19491

Prime factors of 19491 are 3, 73, 89. Prime factorization of 19491 in exponential form is:

19491 = 3¹ × 73¹ × 89¹

Step-2: 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-3: Factors of 19491

List of positive integer factors of 19491 that divides 19491 without a remainder.

1, 3, 73, 89, 219, 267, 6497

Step-4: Factors of 19500

List of positive integer factors of 19500 that divides 19491 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19491 and 19500. The biggest common factor number is the GCF number.
So the greatest common factor 19491 and 19500 is 3.

Also check out the Least Common Multiple of 19491 and 19500