What is the Greatest Common Factor of 74188 and 74205?

Greatest common factor (GCF) of 74188 and 74205 is 17.

GCF(74188,74205) = 17

We will now calculate the prime factors of 74188 and 74205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74188 and 74205.

How to find the GCF of 74188 and 74205?

We will first find the prime factorization of 74188 and 74205. After we will calculate the factors of 74188 and 74205 and find the biggest common factor number .

Step-1: Prime Factorization of 74188

Prime factors of 74188 are 2, 17, 1091. Prime factorization of 74188 in exponential form is:

74188 = 2² × 17¹ × 1091¹

Step-2: 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-3: Factors of 74188

List of positive integer factors of 74188 that divides 74188 without a remainder.

1, 2, 4, 17, 34, 68, 1091, 2182, 4364, 18547, 37094

Step-4: Factors of 74205

List of positive integer factors of 74205 that divides 74188 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74188 and 74205. The biggest common factor number is the GCF number.
So the greatest common factor 74188 and 74205 is 17.

Also check out the Least Common Multiple of 74188 and 74205