What is the Greatest Common Factor of 37254 and 37268?

Greatest common factor (GCF) of 37254 and 37268 is 14.

GCF(37254,37268) = 14

We will now calculate the prime factors of 37254 and 37268, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37254 and 37268.

How to find the GCF of 37254 and 37268?

We will first find the prime factorization of 37254 and 37268. After we will calculate the factors of 37254 and 37268 and find the biggest common factor number .

Step-1: Prime Factorization of 37254

Prime factors of 37254 are 2, 3, 7, 887. Prime factorization of 37254 in exponential form is:

37254 = 2¹ × 3¹ × 7¹ × 887¹

Step-2: Prime Factorization of 37268

Prime factors of 37268 are 2, 7, 11. Prime factorization of 37268 in exponential form is:

37268 = 2² × 7¹ × 11³

Step-3: Factors of 37254

List of positive integer factors of 37254 that divides 37254 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 887, 1774, 2661, 5322, 6209, 12418, 18627

Step-4: Factors of 37268

List of positive integer factors of 37268 that divides 37254 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 121, 154, 242, 308, 484, 847, 1331, 1694, 2662, 3388, 5324, 9317, 18634

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37254 and 37268. The biggest common factor number is the GCF number.
So the greatest common factor 37254 and 37268 is 14.

Also check out the Least Common Multiple of 37254 and 37268