What is the Greatest Common Factor of 37569 and 37584?

Greatest common factor (GCF) of 37569 and 37584 is 3.

GCF(37569,37584) = 3

We will now calculate the prime factors of 37569 and 37584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37569 and 37584.

How to find the GCF of 37569 and 37584?

We will first find the prime factorization of 37569 and 37584. After we will calculate the factors of 37569 and 37584 and find the biggest common factor number .

Step-1: Prime Factorization of 37569

Prime factors of 37569 are 3, 7, 1789. Prime factorization of 37569 in exponential form is:

37569 = 3¹ × 7¹ × 1789¹

Step-2: Prime Factorization of 37584

Prime factors of 37584 are 2, 3, 29. Prime factorization of 37584 in exponential form is:

37584 = 2⁴ × 3⁴ × 29¹

Step-3: Factors of 37569

List of positive integer factors of 37569 that divides 37569 without a remainder.

1, 3, 7, 21, 1789, 5367, 12523

Step-4: Factors of 37584

List of positive integer factors of 37584 that divides 37569 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 29, 36, 48, 54, 58, 72, 81, 87, 108, 116, 144, 162, 174, 216, 232, 261, 324, 348, 432, 464, 522, 648, 696, 783, 1044, 1296, 1392, 1566, 2088, 2349, 3132, 4176, 4698, 6264, 9396, 12528, 18792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37569 and 37584. The biggest common factor number is the GCF number.
So the greatest common factor 37569 and 37584 is 3.

Also check out the Least Common Multiple of 37569 and 37584