What is the Greatest Common Factor of 32209 and 32214?

Greatest common factor (GCF) of 32209 and 32214 is 1.

GCF(32209,32214) = 1

We will now calculate the prime factors of 32209 and 32214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32209 and 32214.

How to find the GCF of 32209 and 32214?

We will first find the prime factorization of 32209 and 32214. After we will calculate the factors of 32209 and 32214 and find the biggest common factor number .

Step-1: Prime Factorization of 32209

Prime factors of 32209 are 31, 1039. Prime factorization of 32209 in exponential form is:

32209 = 31¹ × 1039¹

Step-2: Prime Factorization of 32214

Prime factors of 32214 are 2, 3, 7, 13, 59. Prime factorization of 32214 in exponential form is:

32214 = 2¹ × 3¹ × 7¹ × 13¹ × 59¹

Step-3: Factors of 32209

List of positive integer factors of 32209 that divides 32209 without a remainder.

1, 31, 1039

Step-4: Factors of 32214

List of positive integer factors of 32214 that divides 32209 without a remainder.

1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 59, 78, 91, 118, 177, 182, 273, 354, 413, 546, 767, 826, 1239, 1534, 2301, 2478, 4602, 5369, 10738, 16107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32209 and 32214. The biggest common factor number is the GCF number.
So the greatest common factor 32209 and 32214 is 1.

Also check out the Least Common Multiple of 32209 and 32214