What is the Greatest Common Factor of 37290 and 37305?

Greatest common factor (GCF) of 37290 and 37305 is 15.

GCF(37290,37305) = 15

We will now calculate the prime factors of 37290 and 37305, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37290 and 37305.

How to find the GCF of 37290 and 37305?

We will first find the prime factorization of 37290 and 37305. After we will calculate the factors of 37290 and 37305 and find the biggest common factor number .

Step-1: Prime Factorization of 37290

Prime factors of 37290 are 2, 3, 5, 11, 113. Prime factorization of 37290 in exponential form is:

37290 = 2¹ × 3¹ × 5¹ × 11¹ × 113¹

Step-2: 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-3: Factors of 37290

List of positive integer factors of 37290 that divides 37290 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 113, 165, 226, 330, 339, 565, 678, 1130, 1243, 1695, 2486, 3390, 3729, 6215, 7458, 12430, 18645

Step-4: Factors of 37305

List of positive integer factors of 37305 that divides 37290 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37290 and 37305. The biggest common factor number is the GCF number.
So the greatest common factor 37290 and 37305 is 15.

Also check out the Least Common Multiple of 37290 and 37305