What is the Greatest Common Factor of 39688 and 39708?

Greatest common factor (GCF) of 39688 and 39708 is 4.

GCF(39688,39708) = 4

We will now calculate the prime factors of 39688 and 39708, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39688 and 39708.

How to find the GCF of 39688 and 39708?

We will first find the prime factorization of 39688 and 39708. After we will calculate the factors of 39688 and 39708 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39708

Prime factors of 39708 are 2, 3, 1103. Prime factorization of 39708 in exponential form is:

39708 = 2² × 3² × 1103¹

Step-3: Factors of 39688

List of positive integer factors of 39688 that divides 39688 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

Step-4: Factors of 39708

List of positive integer factors of 39708 that divides 39688 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1103, 2206, 3309, 4412, 6618, 9927, 13236, 19854

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39688 and 39708. The biggest common factor number is the GCF number.
So the greatest common factor 39688 and 39708 is 4.

Also check out the Least Common Multiple of 39688 and 39708