What is the Greatest Common Factor of 75205 and 75220?

Greatest common factor (GCF) of 75205 and 75220 is 5.

GCF(75205,75220) = 5

We will now calculate the prime factors of 75205 and 75220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75205 and 75220.

How to find the GCF of 75205 and 75220?

We will first find the prime factorization of 75205 and 75220. After we will calculate the factors of 75205 and 75220 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 75220

Prime factors of 75220 are 2, 5, 3761. Prime factorization of 75220 in exponential form is:

75220 = 2² × 5¹ × 3761¹

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 75220

List of positive integer factors of 75220 that divides 75205 without a remainder.

1, 2, 4, 5, 10, 20, 3761, 7522, 15044, 18805, 37610

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75205 and 75220. The biggest common factor number is the GCF number.
So the greatest common factor 75205 and 75220 is 5.

Also check out the Least Common Multiple of 75205 and 75220