What is the Greatest Common Factor of 20209 and 20216?

Greatest common factor (GCF) of 20209 and 20216 is 7.

GCF(20209,20216) = 7

We will now calculate the prime factors of 20209 and 20216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20209 and 20216.

How to find the GCF of 20209 and 20216?

We will first find the prime factorization of 20209 and 20216. After we will calculate the factors of 20209 and 20216 and find the biggest common factor number .

Step-1: Prime Factorization of 20209

Prime factors of 20209 are 7, 2887. Prime factorization of 20209 in exponential form is:

20209 = 7¹ × 2887¹

Step-2: Prime Factorization of 20216

Prime factors of 20216 are 2, 7, 19. Prime factorization of 20216 in exponential form is:

20216 = 2³ × 7¹ × 19²

Step-3: Factors of 20209

List of positive integer factors of 20209 that divides 20209 without a remainder.

1, 7, 2887

Step-4: Factors of 20216

List of positive integer factors of 20216 that divides 20209 without a remainder.

1, 2, 4, 7, 8, 14, 19, 28, 38, 56, 76, 133, 152, 266, 361, 532, 722, 1064, 1444, 2527, 2888, 5054, 10108

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20209 and 20216. The biggest common factor number is the GCF number.
So the greatest common factor 20209 and 20216 is 7.

Also check out the Least Common Multiple of 20209 and 20216