What is the Greatest Common Factor of 51205 and 51219?

Greatest common factor (GCF) of 51205 and 51219 is 7.

GCF(51205,51219) = 7

We will now calculate the prime factors of 51205 and 51219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51205 and 51219.

How to find the GCF of 51205 and 51219?

We will first find the prime factorization of 51205 and 51219. After we will calculate the factors of 51205 and 51219 and find the biggest common factor number .

Step-1: Prime Factorization of 51205

Prime factors of 51205 are 5, 7, 11, 19. Prime factorization of 51205 in exponential form is:

51205 = 5¹ × 7² × 11¹ × 19¹

Step-2: Prime Factorization of 51219

Prime factors of 51219 are 3, 7, 271. Prime factorization of 51219 in exponential form is:

51219 = 3³ × 7¹ × 271¹

Step-3: Factors of 51205

List of positive integer factors of 51205 that divides 51205 without a remainder.

1, 5, 7, 11, 19, 35, 49, 55, 77, 95, 133, 209, 245, 385, 539, 665, 931, 1045, 1463, 2695, 4655, 7315, 10241

Step-4: Factors of 51219

List of positive integer factors of 51219 that divides 51205 without a remainder.

1, 3, 7, 9, 21, 27, 63, 189, 271, 813, 1897, 2439, 5691, 7317, 17073

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51205 and 51219. The biggest common factor number is the GCF number.
So the greatest common factor 51205 and 51219 is 7.

Also check out the Least Common Multiple of 51205 and 51219