What is the Greatest Common Factor of 37005 and 37014?

Greatest common factor (GCF) of 37005 and 37014 is 3.

GCF(37005,37014) = 3

We will now calculate the prime factors of 37005 and 37014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37005 and 37014.

How to find the GCF of 37005 and 37014?

We will first find the prime factorization of 37005 and 37014. After we will calculate the factors of 37005 and 37014 and find the biggest common factor number .

Step-1: Prime Factorization of 37005

Prime factors of 37005 are 3, 5, 2467. Prime factorization of 37005 in exponential form is:

37005 = 3¹ × 5¹ × 2467¹

Step-2: Prime Factorization of 37014

Prime factors of 37014 are 2, 3, 31, 199. Prime factorization of 37014 in exponential form is:

37014 = 2¹ × 3¹ × 31¹ × 199¹

Step-3: Factors of 37005

List of positive integer factors of 37005 that divides 37005 without a remainder.

1, 3, 5, 15, 2467, 7401, 12335

Step-4: Factors of 37014

List of positive integer factors of 37014 that divides 37005 without a remainder.

1, 2, 3, 6, 31, 62, 93, 186, 199, 398, 597, 1194, 6169, 12338, 18507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37005 and 37014. The biggest common factor number is the GCF number.
So the greatest common factor 37005 and 37014 is 3.

Also check out the Least Common Multiple of 37005 and 37014