What is the Greatest Common Factor of 37854 and 37872?

Greatest common factor (GCF) of 37854 and 37872 is 18.

GCF(37854,37872) = 18

We will now calculate the prime factors of 37854 and 37872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37854 and 37872.

How to find the GCF of 37854 and 37872?

We will first find the prime factorization of 37854 and 37872. After we will calculate the factors of 37854 and 37872 and find the biggest common factor number .

Step-1: Prime Factorization of 37854

Prime factors of 37854 are 2, 3, 701. Prime factorization of 37854 in exponential form is:

37854 = 2¹ × 3³ × 701¹

Step-2: Prime Factorization of 37872

Prime factors of 37872 are 2, 3, 263. Prime factorization of 37872 in exponential form is:

37872 = 2⁴ × 3² × 263¹

Step-3: Factors of 37854

List of positive integer factors of 37854 that divides 37854 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 701, 1402, 2103, 4206, 6309, 12618, 18927

Step-4: Factors of 37872

List of positive integer factors of 37872 that divides 37854 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 263, 526, 789, 1052, 1578, 2104, 2367, 3156, 4208, 4734, 6312, 9468, 12624, 18936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37854 and 37872. The biggest common factor number is the GCF number.
So the greatest common factor 37854 and 37872 is 18.

Also check out the Least Common Multiple of 37854 and 37872