What is the Greatest Common Factor of 37184 and 37198?

Greatest common factor (GCF) of 37184 and 37198 is 14.

GCF(37184,37198) = 14

We will now calculate the prime factors of 37184 and 37198, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37184 and 37198.

How to find the GCF of 37184 and 37198?

We will first find the prime factorization of 37184 and 37198. After we will calculate the factors of 37184 and 37198 and find the biggest common factor number .

Step-1: Prime Factorization of 37184

Prime factors of 37184 are 2, 7, 83. Prime factorization of 37184 in exponential form is:

37184 = 2⁶ × 7¹ × 83¹

Step-2: Prime Factorization of 37198

Prime factors of 37198 are 2, 7, 2657. Prime factorization of 37198 in exponential form is:

37198 = 2¹ × 7¹ × 2657¹

Step-3: Factors of 37184

List of positive integer factors of 37184 that divides 37184 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 83, 112, 166, 224, 332, 448, 581, 664, 1162, 1328, 2324, 2656, 4648, 5312, 9296, 18592

Step-4: Factors of 37198

List of positive integer factors of 37198 that divides 37184 without a remainder.

1, 2, 7, 14, 2657, 5314, 18599

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37184 and 37198. The biggest common factor number is the GCF number.
So the greatest common factor 37184 and 37198 is 14.

Also check out the Least Common Multiple of 37184 and 37198