What is the Greatest Common Factor of 75205 and 75216?

Greatest common factor (GCF) of 75205 and 75216 is 1.

GCF(75205,75216) = 1

We will now calculate the prime factors of 75205 and 75216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75205 and 75216.

How to find the GCF of 75205 and 75216?

We will first find the prime factorization of 75205 and 75216. After we will calculate the factors of 75205 and 75216 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 75216

Prime factors of 75216 are 2, 3, 1567. Prime factorization of 75216 in exponential form is:

75216 = 2⁴ × 3¹ × 1567¹

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 75216

List of positive integer factors of 75216 that divides 75205 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1567, 3134, 4701, 6268, 9402, 12536, 18804, 25072, 37608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75205 and 75216. The biggest common factor number is the GCF number.
So the greatest common factor 75205 and 75216 is 1.

Also check out the Least Common Multiple of 75205 and 75216