What is the Greatest Common Factor of 37008 and 37014?

Greatest common factor (GCF) of 37008 and 37014 is 6.

GCF(37008,37014) = 6

We will now calculate the prime factors of 37008 and 37014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37008 and 37014.

How to find the GCF of 37008 and 37014?

We will first find the prime factorization of 37008 and 37014. After we will calculate the factors of 37008 and 37014 and find the biggest common factor number .

Step-1: Prime Factorization of 37008

Prime factors of 37008 are 2, 3, 257. Prime factorization of 37008 in exponential form is:

37008 = 2⁴ × 3² × 257¹

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 37008

List of positive integer factors of 37008 that divides 37008 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 257, 514, 771, 1028, 1542, 2056, 2313, 3084, 4112, 4626, 6168, 9252, 12336, 18504

Step-4: Factors of 37014

List of positive integer factors of 37014 that divides 37008 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 37008 and 37014. The biggest common factor number is the GCF number.
So the greatest common factor 37008 and 37014 is 6.

Also check out the Least Common Multiple of 37008 and 37014