What is the Greatest Common Factor of 39088 and 39102?

Greatest common factor (GCF) of 39088 and 39102 is 14.

GCF(39088,39102) = 14

We will now calculate the prime factors of 39088 and 39102, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39088 and 39102.

How to find the GCF of 39088 and 39102?

We will first find the prime factorization of 39088 and 39102. After we will calculate the factors of 39088 and 39102 and find the biggest common factor number .

Step-1: Prime Factorization of 39088

Prime factors of 39088 are 2, 7, 349. Prime factorization of 39088 in exponential form is:

39088 = 2⁴ × 7¹ × 349¹

Step-2: Prime Factorization of 39102

Prime factors of 39102 are 2, 3, 7, 19. Prime factorization of 39102 in exponential form is:

39102 = 2¹ × 3¹ × 7³ × 19¹

Step-3: Factors of 39088

List of positive integer factors of 39088 that divides 39088 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 349, 698, 1396, 2443, 2792, 4886, 5584, 9772, 19544

Step-4: Factors of 39102

List of positive integer factors of 39102 that divides 39088 without a remainder.

1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 49, 57, 98, 114, 133, 147, 266, 294, 343, 399, 686, 798, 931, 1029, 1862, 2058, 2793, 5586, 6517, 13034, 19551

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39088 and 39102. The biggest common factor number is the GCF number.
So the greatest common factor 39088 and 39102 is 14.

Also check out the Least Common Multiple of 39088 and 39102