What is the Greatest Common Factor of 30209 and 30226?

Greatest common factor (GCF) of 30209 and 30226 is 17.

GCF(30209,30226) = 17

We will now calculate the prime factors of 30209 and 30226, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30209 and 30226.

How to find the GCF of 30209 and 30226?

We will first find the prime factorization of 30209 and 30226. After we will calculate the factors of 30209 and 30226 and find the biggest common factor number .

Step-1: Prime Factorization of 30209

Prime factors of 30209 are 17, 1777. Prime factorization of 30209 in exponential form is:

30209 = 17¹ × 1777¹

Step-2: Prime Factorization of 30226

Prime factors of 30226 are 2, 7, 17, 127. Prime factorization of 30226 in exponential form is:

30226 = 2¹ × 7¹ × 17¹ × 127¹

Step-3: Factors of 30209

List of positive integer factors of 30209 that divides 30209 without a remainder.

1, 17, 1777

Step-4: Factors of 30226

List of positive integer factors of 30226 that divides 30209 without a remainder.

1, 2, 7, 14, 17, 34, 119, 127, 238, 254, 889, 1778, 2159, 4318, 15113

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30209 and 30226. The biggest common factor number is the GCF number.
So the greatest common factor 30209 and 30226 is 17.

Also check out the Least Common Multiple of 30209 and 30226