What is the Greatest Common Factor of 18768 and 18774?

Greatest common factor (GCF) of 18768 and 18774 is 6.

GCF(18768,18774) = 6

We will now calculate the prime factors of 18768 and 18774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 18768 and 18774.

How to find the GCF of 18768 and 18774?

We will first find the prime factorization of 18768 and 18774. After we will calculate the factors of 18768 and 18774 and find the biggest common factor number .

Step-1: Prime Factorization of 18768

Prime factors of 18768 are 2, 3, 17, 23. Prime factorization of 18768 in exponential form is:

18768 = 2⁴ × 3¹ × 17¹ × 23¹

Step-2: Prime Factorization of 18774

Prime factors of 18774 are 2, 3, 7, 149. Prime factorization of 18774 in exponential form is:

18774 = 2¹ × 3² × 7¹ × 149¹

Step-3: Factors of 18768

List of positive integer factors of 18768 that divides 18768 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 23, 24, 34, 46, 48, 51, 68, 69, 92, 102, 136, 138, 184, 204, 272, 276, 368, 391, 408, 552, 782, 816, 1104, 1173, 1564, 2346, 3128, 4692, 6256, 9384

Step-4: Factors of 18774

List of positive integer factors of 18774 that divides 18768 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 149, 298, 447, 894, 1043, 1341, 2086, 2682, 3129, 6258, 9387

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 18768 and 18774. The biggest common factor number is the GCF number.
So the greatest common factor 18768 and 18774 is 6.

Also check out the Least Common Multiple of 18768 and 18774