What is the Greatest Common Factor of 34209 and 34216?

Greatest common factor (GCF) of 34209 and 34216 is 7.

GCF(34209,34216) = 7

We will now calculate the prime factors of 34209 and 34216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34209 and 34216.

How to find the GCF of 34209 and 34216?

We will first find the prime factorization of 34209 and 34216. After we will calculate the factors of 34209 and 34216 and find the biggest common factor number .

Step-1: Prime Factorization of 34209

Prime factors of 34209 are 3, 7, 181. Prime factorization of 34209 in exponential form is:

34209 = 3³ × 7¹ × 181¹

Step-2: Prime Factorization of 34216

Prime factors of 34216 are 2, 7, 13, 47. Prime factorization of 34216 in exponential form is:

34216 = 2³ × 7¹ × 13¹ × 47¹

Step-3: Factors of 34209

List of positive integer factors of 34209 that divides 34209 without a remainder.

1, 3, 7, 9, 21, 27, 63, 181, 189, 543, 1267, 1629, 3801, 4887, 11403

Step-4: Factors of 34216

List of positive integer factors of 34216 that divides 34209 without a remainder.

1, 2, 4, 7, 8, 13, 14, 26, 28, 47, 52, 56, 91, 94, 104, 182, 188, 329, 364, 376, 611, 658, 728, 1222, 1316, 2444, 2632, 4277, 4888, 8554, 17108

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34209 and 34216. The biggest common factor number is the GCF number.
So the greatest common factor 34209 and 34216 is 7.

Also check out the Least Common Multiple of 34209 and 34216