What is the Greatest Common Factor of 20519 and 20538?

Greatest common factor (GCF) of 20519 and 20538 is 1.

GCF(20519,20538) = 1

We will now calculate the prime factors of 20519 and 20538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20519 and 20538.

How to find the GCF of 20519 and 20538?

We will first find the prime factorization of 20519 and 20538. After we will calculate the factors of 20519 and 20538 and find the biggest common factor number .

Step-1: Prime Factorization of 20519

Prime factors of 20519 are 17, 71. Prime factorization of 20519 in exponential form is:

20519 = 17² × 71¹

Step-2: Prime Factorization of 20538

Prime factors of 20538 are 2, 3, 7, 163. Prime factorization of 20538 in exponential form is:

20538 = 2¹ × 3² × 7¹ × 163¹

Step-3: Factors of 20519

List of positive integer factors of 20519 that divides 20519 without a remainder.

1, 17, 71, 289, 1207

Step-4: Factors of 20538

List of positive integer factors of 20538 that divides 20519 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 163, 326, 489, 978, 1141, 1467, 2282, 2934, 3423, 6846, 10269

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20519 and 20538. The biggest common factor number is the GCF number.
So the greatest common factor 20519 and 20538 is 1.

Also check out the Least Common Multiple of 20519 and 20538