What is the Greatest Common Factor of 37746 and 37764?

Greatest common factor (GCF) of 37746 and 37764 is 18.

GCF(37746,37764) = 18

We will now calculate the prime factors of 37746 and 37764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37746 and 37764.

How to find the GCF of 37746 and 37764?

We will first find the prime factorization of 37746 and 37764. After we will calculate the factors of 37746 and 37764 and find the biggest common factor number .

Step-1: Prime Factorization of 37746

Prime factors of 37746 are 2, 3, 233. Prime factorization of 37746 in exponential form is:

37746 = 2¹ × 3⁴ × 233¹

Step-2: Prime Factorization of 37764

Prime factors of 37764 are 2, 3, 1049. Prime factorization of 37764 in exponential form is:

37764 = 2² × 3² × 1049¹

Step-3: Factors of 37746

List of positive integer factors of 37746 that divides 37746 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 233, 466, 699, 1398, 2097, 4194, 6291, 12582, 18873

Step-4: Factors of 37764

List of positive integer factors of 37764 that divides 37746 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1049, 2098, 3147, 4196, 6294, 9441, 12588, 18882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37746 and 37764. The biggest common factor number is the GCF number.
So the greatest common factor 37746 and 37764 is 18.

Also check out the Least Common Multiple of 37746 and 37764