What is the Greatest Common Factor of 17038 and 17052?

Greatest common factor (GCF) of 17038 and 17052 is 14.

GCF(17038,17052) = 14

We will now calculate the prime factors of 17038 and 17052, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17038 and 17052.

How to find the GCF of 17038 and 17052?

We will first find the prime factorization of 17038 and 17052. After we will calculate the factors of 17038 and 17052 and find the biggest common factor number .

Step-1: Prime Factorization of 17038

Prime factors of 17038 are 2, 7, 1217. Prime factorization of 17038 in exponential form is:

17038 = 2¹ × 7¹ × 1217¹

Step-2: Prime Factorization of 17052

Prime factors of 17052 are 2, 3, 7, 29. Prime factorization of 17052 in exponential form is:

17052 = 2² × 3¹ × 7² × 29¹

Step-3: Factors of 17038

List of positive integer factors of 17038 that divides 17038 without a remainder.

1, 2, 7, 14, 1217, 2434, 8519

Step-4: Factors of 17052

List of positive integer factors of 17052 that divides 17038 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 29, 42, 49, 58, 84, 87, 98, 116, 147, 174, 196, 203, 294, 348, 406, 588, 609, 812, 1218, 1421, 2436, 2842, 4263, 5684, 8526

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17038 and 17052. The biggest common factor number is the GCF number.
So the greatest common factor 17038 and 17052 is 14.

Also check out the Least Common Multiple of 17038 and 17052