What is the Greatest Common Factor of 39114 and 39123?

Greatest common factor (GCF) of 39114 and 39123 is 9.

GCF(39114,39123) = 9

We will now calculate the prime factors of 39114 and 39123, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39114 and 39123.

How to find the GCF of 39114 and 39123?

We will first find the prime factorization of 39114 and 39123. After we will calculate the factors of 39114 and 39123 and find the biggest common factor number .

Step-1: Prime Factorization of 39114

Prime factors of 39114 are 2, 3, 41, 53. Prime factorization of 39114 in exponential form is:

39114 = 2¹ × 3² × 41¹ × 53¹

Step-2: Prime Factorization of 39123

Prime factors of 39123 are 3, 7, 23. Prime factorization of 39123 in exponential form is:

39123 = 3⁵ × 7¹ × 23¹

Step-3: Factors of 39114

List of positive integer factors of 39114 that divides 39114 without a remainder.

1, 2, 3, 6, 9, 18, 41, 53, 82, 106, 123, 159, 246, 318, 369, 477, 738, 954, 2173, 4346, 6519, 13038, 19557

Step-4: Factors of 39123

List of positive integer factors of 39123 that divides 39114 without a remainder.

1, 3, 7, 9, 21, 23, 27, 63, 69, 81, 161, 189, 207, 243, 483, 567, 621, 1449, 1701, 1863, 4347, 5589, 13041

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39114 and 39123. The biggest common factor number is the GCF number.
So the greatest common factor 39114 and 39123 is 9.

Also check out the Least Common Multiple of 39114 and 39123