What is the Greatest Common Factor of 17225 and 17238?

Greatest common factor (GCF) of 17225 and 17238 is 13.

GCF(17225,17238) = 13

We will now calculate the prime factors of 17225 and 17238, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17225 and 17238.

How to find the GCF of 17225 and 17238?

We will first find the prime factorization of 17225 and 17238. After we will calculate the factors of 17225 and 17238 and find the biggest common factor number .

Step-1: Prime Factorization of 17225

Prime factors of 17225 are 5, 13, 53. Prime factorization of 17225 in exponential form is:

17225 = 5² × 13¹ × 53¹

Step-2: Prime Factorization of 17238

Prime factors of 17238 are 2, 3, 13, 17. Prime factorization of 17238 in exponential form is:

17238 = 2¹ × 3¹ × 13² × 17¹

Step-3: Factors of 17225

List of positive integer factors of 17225 that divides 17225 without a remainder.

1, 5, 13, 25, 53, 65, 265, 325, 689, 1325, 3445

Step-4: Factors of 17238

List of positive integer factors of 17238 that divides 17225 without a remainder.

1, 2, 3, 6, 13, 17, 26, 34, 39, 51, 78, 102, 169, 221, 338, 442, 507, 663, 1014, 1326, 2873, 5746, 8619

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17225 and 17238. The biggest common factor number is the GCF number.
So the greatest common factor 17225 and 17238 is 13.

Also check out the Least Common Multiple of 17225 and 17238