What is the Greatest Common Factor of 37278 and 37297?

Greatest common factor (GCF) of 37278 and 37297 is 19.

GCF(37278,37297) = 19

We will now calculate the prime factors of 37278 and 37297, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37278 and 37297.

How to find the GCF of 37278 and 37297?

We will first find the prime factorization of 37278 and 37297. After we will calculate the factors of 37278 and 37297 and find the biggest common factor number .

Step-1: Prime Factorization of 37278

Prime factors of 37278 are 2, 3, 19, 109. Prime factorization of 37278 in exponential form is:

37278 = 2¹ × 3² × 19¹ × 109¹

Step-2: Prime Factorization of 37297

Prime factors of 37297 are 13, 19, 151. Prime factorization of 37297 in exponential form is:

37297 = 13¹ × 19¹ × 151¹

Step-3: Factors of 37278

List of positive integer factors of 37278 that divides 37278 without a remainder.

1, 2, 3, 6, 9, 18, 19, 38, 57, 109, 114, 171, 218, 327, 342, 654, 981, 1962, 2071, 4142, 6213, 12426, 18639

Step-4: Factors of 37297

List of positive integer factors of 37297 that divides 37278 without a remainder.

1, 13, 19, 151, 247, 1963, 2869

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37278 and 37297. The biggest common factor number is the GCF number.
So the greatest common factor 37278 and 37297 is 19.

Also check out the Least Common Multiple of 37278 and 37297