What is the Greatest Common Factor of 19500 and 19510?

Greatest common factor (GCF) of 19500 and 19510 is 10.

GCF(19500,19510) = 10

We will now calculate the prime factors of 19500 and 19510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19500 and 19510.

How to find the GCF of 19500 and 19510?

We will first find the prime factorization of 19500 and 19510. After we will calculate the factors of 19500 and 19510 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 19510

Prime factors of 19510 are 2, 5, 1951. Prime factorization of 19510 in exponential form is:

19510 = 2¹ × 5¹ × 1951¹

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 19510

List of positive integer factors of 19510 that divides 19500 without a remainder.

1, 2, 5, 10, 1951, 3902, 9755

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19500 and 19510. The biggest common factor number is the GCF number.
So the greatest common factor 19500 and 19510 is 10.

Also check out the Least Common Multiple of 19500 and 19510