What is the Greatest Common Factor of 37305 and 37310?

Greatest common factor (GCF) of 37305 and 37310 is 5.

GCF(37305,37310) = 5

We will now calculate the prime factors of 37305 and 37310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37305 and 37310.

How to find the GCF of 37305 and 37310?

We will first find the prime factorization of 37305 and 37310. After we will calculate the factors of 37305 and 37310 and find the biggest common factor number .

Step-1: Prime Factorization of 37305

Prime factors of 37305 are 3, 5, 829. Prime factorization of 37305 in exponential form is:

37305 = 3² × 5¹ × 829¹

Step-2: Prime Factorization of 37310

Prime factors of 37310 are 2, 5, 7, 13, 41. Prime factorization of 37310 in exponential form is:

37310 = 2¹ × 5¹ × 7¹ × 13¹ × 41¹

Step-3: Factors of 37305

List of positive integer factors of 37305 that divides 37305 without a remainder.

1, 3, 5, 9, 15, 45, 829, 2487, 4145, 7461, 12435

Step-4: Factors of 37310

List of positive integer factors of 37310 that divides 37305 without a remainder.

1, 2, 5, 7, 10, 13, 14, 26, 35, 41, 65, 70, 82, 91, 130, 182, 205, 287, 410, 455, 533, 574, 910, 1066, 1435, 2665, 2870, 3731, 5330, 7462, 18655

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37305 and 37310. The biggest common factor number is the GCF number.
So the greatest common factor 37305 and 37310 is 5.

Also check out the Least Common Multiple of 37305 and 37310