What is the Greatest Common Factor of 75205 and 75218?

Greatest common factor (GCF) of 75205 and 75218 is 13.

GCF(75205,75218) = 13

We will now calculate the prime factors of 75205 and 75218, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75205 and 75218.

How to find the GCF of 75205 and 75218?

We will first find the prime factorization of 75205 and 75218. After we will calculate the factors of 75205 and 75218 and find the biggest common factor number .

Step-1: Prime Factorization of 75205

Prime factors of 75205 are 5, 13, 89. Prime factorization of 75205 in exponential form is:

75205 = 5¹ × 13² × 89¹

Step-2: Prime Factorization of 75218

Prime factors of 75218 are 2, 11, 13, 263. Prime factorization of 75218 in exponential form is:

75218 = 2¹ × 11¹ × 13¹ × 263¹

Step-3: Factors of 75205

List of positive integer factors of 75205 that divides 75205 without a remainder.

1, 5, 13, 65, 89, 169, 445, 845, 1157, 5785, 15041

Step-4: Factors of 75218

List of positive integer factors of 75218 that divides 75205 without a remainder.

1, 2, 11, 13, 22, 26, 143, 263, 286, 526, 2893, 3419, 5786, 6838, 37609

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75205 and 75218. The biggest common factor number is the GCF number.
So the greatest common factor 75205 and 75218 is 13.

Also check out the Least Common Multiple of 75205 and 75218