What is the Greatest Common Factor of 19509 and 19516?

Greatest common factor (GCF) of 19509 and 19516 is 7.

GCF(19509,19516) = 7

We will now calculate the prime factors of 19509 and 19516, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19509 and 19516.

How to find the GCF of 19509 and 19516?

We will first find the prime factorization of 19509 and 19516. After we will calculate the factors of 19509 and 19516 and find the biggest common factor number .

Step-1: Prime Factorization of 19509

Prime factors of 19509 are 3, 7, 929. Prime factorization of 19509 in exponential form is:

19509 = 3¹ × 7¹ × 929¹

Step-2: Prime Factorization of 19516

Prime factors of 19516 are 2, 7, 17, 41. Prime factorization of 19516 in exponential form is:

19516 = 2² × 7¹ × 17¹ × 41¹

Step-3: Factors of 19509

List of positive integer factors of 19509 that divides 19509 without a remainder.

1, 3, 7, 21, 929, 2787, 6503

Step-4: Factors of 19516

List of positive integer factors of 19516 that divides 19509 without a remainder.

1, 2, 4, 7, 14, 17, 28, 34, 41, 68, 82, 119, 164, 238, 287, 476, 574, 697, 1148, 1394, 2788, 4879, 9758

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19509 and 19516. The biggest common factor number is the GCF number.
So the greatest common factor 19509 and 19516 is 7.

Also check out the Least Common Multiple of 19509 and 19516