What is the Greatest Common Factor of 35209 and 35217?

Greatest common factor (GCF) of 35209 and 35217 is 1.

GCF(35209,35217) = 1

We will now calculate the prime factors of 35209 and 35217, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35209 and 35217.

How to find the GCF of 35209 and 35217?

We will first find the prime factorization of 35209 and 35217. After we will calculate the factors of 35209 and 35217 and find the biggest common factor number .

Step-1: Prime Factorization of 35209

Prime factors of 35209 are 137, 257. Prime factorization of 35209 in exponential form is:

35209 = 137¹ × 257¹

Step-2: Prime Factorization of 35217

Prime factors of 35217 are 3, 7, 13, 43. Prime factorization of 35217 in exponential form is:

35217 = 3² × 7¹ × 13¹ × 43¹

Step-3: Factors of 35209

List of positive integer factors of 35209 that divides 35209 without a remainder.

1, 137, 257

Step-4: Factors of 35217

List of positive integer factors of 35217 that divides 35209 without a remainder.

1, 3, 7, 9, 13, 21, 39, 43, 63, 91, 117, 129, 273, 301, 387, 559, 819, 903, 1677, 2709, 3913, 5031, 11739

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35209 and 35217. The biggest common factor number is the GCF number.
So the greatest common factor 35209 and 35217 is 1.

Also check out the Least Common Multiple of 35209 and 35217