What is the Greatest Common Factor of 37254 and 37264?

Greatest common factor (GCF) of 37254 and 37264 is 2.

GCF(37254,37264) = 2

We will now calculate the prime factors of 37254 and 37264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37254 and 37264.

How to find the GCF of 37254 and 37264?

We will first find the prime factorization of 37254 and 37264. After we will calculate the factors of 37254 and 37264 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 37264

Prime factors of 37264 are 2, 17, 137. Prime factorization of 37264 in exponential form is:

37264 = 2⁴ × 17¹ × 137¹

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 37264

List of positive integer factors of 37264 that divides 37254 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136, 137, 272, 274, 548, 1096, 2192, 2329, 4658, 9316, 18632

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37254 and 37264. The biggest common factor number is the GCF number.
So the greatest common factor 37254 and 37264 is 2.

Also check out the Least Common Multiple of 37254 and 37264