What is the Greatest Common Factor of 37259 and 37278?

Greatest common factor (GCF) of 37259 and 37278 is 19.

GCF(37259,37278) = 19

We will now calculate the prime factors of 37259 and 37278, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37259 and 37278.

How to find the GCF of 37259 and 37278?

We will first find the prime factorization of 37259 and 37278. After we will calculate the factors of 37259 and 37278 and find the biggest common factor number .

Step-1: Prime Factorization of 37259

Prime factors of 37259 are 19, 37, 53. Prime factorization of 37259 in exponential form is:

37259 = 19¹ × 37¹ × 53¹

Step-2: 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-3: Factors of 37259

List of positive integer factors of 37259 that divides 37259 without a remainder.

1, 19, 37, 53, 703, 1007, 1961

Step-4: Factors of 37278

List of positive integer factors of 37278 that divides 37259 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37259 and 37278. The biggest common factor number is the GCF number.
So the greatest common factor 37259 and 37278 is 19.

Also check out the Least Common Multiple of 37259 and 37278