What is the Greatest Common Factor of 39678 and 39688?

Greatest common factor (GCF) of 39678 and 39688 is 2.

GCF(39678,39688) = 2

We will now calculate the prime factors of 39678 and 39688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39678 and 39688.

How to find the GCF of 39678 and 39688?

We will first find the prime factorization of 39678 and 39688. After we will calculate the factors of 39678 and 39688 and find the biggest common factor number .

Step-1: Prime Factorization of 39678

Prime factors of 39678 are 2, 3, 17, 389. Prime factorization of 39678 in exponential form is:

39678 = 2¹ × 3¹ × 17¹ × 389¹

Step-2: Prime Factorization of 39688

Prime factors of 39688 are 2, 11, 41. Prime factorization of 39688 in exponential form is:

39688 = 2³ × 11² × 41¹

Step-3: Factors of 39678

List of positive integer factors of 39678 that divides 39678 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 389, 778, 1167, 2334, 6613, 13226, 19839

Step-4: Factors of 39688

List of positive integer factors of 39688 that divides 39678 without a remainder.

1, 2, 4, 8, 11, 22, 41, 44, 82, 88, 121, 164, 242, 328, 451, 484, 902, 968, 1804, 3608, 4961, 9922, 19844

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39678 and 39688. The biggest common factor number is the GCF number.
So the greatest common factor 39678 and 39688 is 2.

Also check out the Least Common Multiple of 39678 and 39688