What is the Greatest Common Factor of 37638 and 37654?

Greatest common factor (GCF) of 37638 and 37654 is 2.

GCF(37638,37654) = 2

We will now calculate the prime factors of 37638 and 37654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37638 and 37654.

How to find the GCF of 37638 and 37654?

We will first find the prime factorization of 37638 and 37654. After we will calculate the factors of 37638 and 37654 and find the biggest common factor number .

Step-1: Prime Factorization of 37638

Prime factors of 37638 are 2, 3, 17, 41. Prime factorization of 37638 in exponential form is:

37638 = 2¹ × 3³ × 17¹ × 41¹

Step-2: Prime Factorization of 37654

Prime factors of 37654 are 2, 67, 281. Prime factorization of 37654 in exponential form is:

37654 = 2¹ × 67¹ × 281¹

Step-3: Factors of 37638

List of positive integer factors of 37638 that divides 37638 without a remainder.

1, 2, 3, 6, 9, 17, 18, 27, 34, 41, 51, 54, 82, 102, 123, 153, 246, 306, 369, 459, 697, 738, 918, 1107, 1394, 2091, 2214, 4182, 6273, 12546, 18819

Step-4: Factors of 37654

List of positive integer factors of 37654 that divides 37638 without a remainder.

1, 2, 67, 134, 281, 562, 18827

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37638 and 37654. The biggest common factor number is the GCF number.
So the greatest common factor 37638 and 37654 is 2.

Also check out the Least Common Multiple of 37638 and 37654