What is the Greatest Common Factor of 38692 and 38709?

Greatest common factor (GCF) of 38692 and 38709 is 17.

GCF(38692,38709) = 17

We will now calculate the prime factors of 38692 and 38709, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38692 and 38709.

How to find the GCF of 38692 and 38709?

We will first find the prime factorization of 38692 and 38709. After we will calculate the factors of 38692 and 38709 and find the biggest common factor number .

Step-1: Prime Factorization of 38692

Prime factors of 38692 are 2, 17, 569. Prime factorization of 38692 in exponential form is:

38692 = 2² × 17¹ × 569¹

Step-2: Prime Factorization of 38709

Prime factors of 38709 are 3, 11, 17, 23. Prime factorization of 38709 in exponential form is:

38709 = 3² × 11¹ × 17¹ × 23¹

Step-3: Factors of 38692

List of positive integer factors of 38692 that divides 38692 without a remainder.

1, 2, 4, 17, 34, 68, 569, 1138, 2276, 9673, 19346

Step-4: Factors of 38709

List of positive integer factors of 38709 that divides 38692 without a remainder.

1, 3, 9, 11, 17, 23, 33, 51, 69, 99, 153, 187, 207, 253, 391, 561, 759, 1173, 1683, 2277, 3519, 4301, 12903

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38692 and 38709. The biggest common factor number is the GCF number.
So the greatest common factor 38692 and 38709 is 17.

Also check out the Least Common Multiple of 38692 and 38709