What is the Greatest Common Factor of 51184 and 51198?

Greatest common factor (GCF) of 51184 and 51198 is 14.

GCF(51184,51198) = 14

We will now calculate the prime factors of 51184 and 51198, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51184 and 51198.

How to find the GCF of 51184 and 51198?

We will first find the prime factorization of 51184 and 51198. After we will calculate the factors of 51184 and 51198 and find the biggest common factor number .

Step-1: Prime Factorization of 51184

Prime factors of 51184 are 2, 7, 457. Prime factorization of 51184 in exponential form is:

51184 = 2⁴ × 7¹ × 457¹

Step-2: 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-3: Factors of 51184

List of positive integer factors of 51184 that divides 51184 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 457, 914, 1828, 3199, 3656, 6398, 7312, 12796, 25592

Step-4: Factors of 51198

List of positive integer factors of 51198 that divides 51184 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51184 and 51198. The biggest common factor number is the GCF number.
So the greatest common factor 51184 and 51198 is 14.

Also check out the Least Common Multiple of 51184 and 51198