What is the Greatest Common Factor of 51198 and 51205?

Greatest common factor (GCF) of 51198 and 51205 is 7.

GCF(51198,51205) = 7

We will now calculate the prime factors of 51198 and 51205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51198 and 51205.

How to find the GCF of 51198 and 51205?

We will first find the prime factorization of 51198 and 51205. After we will calculate the factors of 51198 and 51205 and find the biggest common factor number .

Step-1: Prime Factorization of 51198

Prime factors of 51198 are 2, 3, 7, 23, 53. Prime factorization of 51198 in exponential form is:

51198 = 2¹ × 3¹ × 7¹ × 23¹ × 53¹

Step-2: 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-3: Factors of 51198

List of positive integer factors of 51198 that divides 51198 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 53, 69, 106, 138, 159, 161, 318, 322, 371, 483, 742, 966, 1113, 1219, 2226, 2438, 3657, 7314, 8533, 17066, 25599

Step-4: Factors of 51205

List of positive integer factors of 51205 that divides 51198 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51198 and 51205. The biggest common factor number is the GCF number.
So the greatest common factor 51198 and 51205 is 7.

Also check out the Least Common Multiple of 51198 and 51205