What is the Greatest Common Factor of 32205 and 32214?

Greatest common factor (GCF) of 32205 and 32214 is 3.

GCF(32205,32214) = 3

We will now calculate the prime factors of 32205 and 32214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32205 and 32214.

How to find the GCF of 32205 and 32214?

We will first find the prime factorization of 32205 and 32214. After we will calculate the factors of 32205 and 32214 and find the biggest common factor number .

Step-1: Prime Factorization of 32205

Prime factors of 32205 are 3, 5, 19, 113. Prime factorization of 32205 in exponential form is:

32205 = 3¹ × 5¹ × 19¹ × 113¹

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 32205

List of positive integer factors of 32205 that divides 32205 without a remainder.

1, 3, 5, 15, 19, 57, 95, 113, 285, 339, 565, 1695, 2147, 6441, 10735

Step-4: Factors of 32214

List of positive integer factors of 32214 that divides 32205 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 32205 and 32214. The biggest common factor number is the GCF number.
So the greatest common factor 32205 and 32214 is 3.

Also check out the Least Common Multiple of 32205 and 32214