What is the Greatest Common Factor of 74205 and 74222?

Greatest common factor (GCF) of 74205 and 74222 is 17.

GCF(74205,74222) = 17

We will now calculate the prime factors of 74205 and 74222, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74205 and 74222.

How to find the GCF of 74205 and 74222?

We will first find the prime factorization of 74205 and 74222. After we will calculate the factors of 74205 and 74222 and find the biggest common factor number .

Step-1: Prime Factorization of 74205

Prime factors of 74205 are 3, 5, 17, 97. Prime factorization of 74205 in exponential form is:

74205 = 3² × 5¹ × 17¹ × 97¹

Step-2: Prime Factorization of 74222

Prime factors of 74222 are 2, 17, 37, 59. Prime factorization of 74222 in exponential form is:

74222 = 2¹ × 17¹ × 37¹ × 59¹

Step-3: Factors of 74205

List of positive integer factors of 74205 that divides 74205 without a remainder.

1, 3, 5, 9, 15, 17, 45, 51, 85, 97, 153, 255, 291, 485, 765, 873, 1455, 1649, 4365, 4947, 8245, 14841, 24735

Step-4: Factors of 74222

List of positive integer factors of 74222 that divides 74205 without a remainder.

1, 2, 17, 34, 37, 59, 74, 118, 629, 1003, 1258, 2006, 2183, 4366, 37111

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74205 and 74222. The biggest common factor number is the GCF number.
So the greatest common factor 74205 and 74222 is 17.

Also check out the Least Common Multiple of 74205 and 74222