What is the Greatest Common Factor of 37638 and 37653?

Greatest common factor (GCF) of 37638 and 37653 is 3.

GCF(37638,37653) = 3

We will now calculate the prime factors of 37638 and 37653, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37638 and 37653.

How to find the GCF of 37638 and 37653?

We will first find the prime factorization of 37638 and 37653. After we will calculate the factors of 37638 and 37653 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 37653

Prime factors of 37653 are 3, 7, 11, 163. Prime factorization of 37653 in exponential form is:

37653 = 3¹ × 7¹ × 11¹ × 163¹

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 37653

List of positive integer factors of 37653 that divides 37638 without a remainder.

1, 3, 7, 11, 21, 33, 77, 163, 231, 489, 1141, 1793, 3423, 5379, 12551

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37638 and 37653. The biggest common factor number is the GCF number.
So the greatest common factor 37638 and 37653 is 3.

Also check out the Least Common Multiple of 37638 and 37653