What is the Greatest Common Factor of 5185 and 5205?

Greatest common factor (GCF) of 5185 and 5205 is 5.

GCF(5185,5205) = 5

We will now calculate the prime factors of 5185 and 5205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5185 and 5205.

How to find the GCF of 5185 and 5205?

We will first find the prime factorization of 5185 and 5205. After we will calculate the factors of 5185 and 5205 and find the biggest common factor number .

Step-1: Prime Factorization of 5185

Prime factors of 5185 are 5, 17, 61. Prime factorization of 5185 in exponential form is:

5185 = 5¹ × 17¹ × 61¹

Step-2: Prime Factorization of 5205

Prime factors of 5205 are 3, 5, 347. Prime factorization of 5205 in exponential form is:

5205 = 3¹ × 5¹ × 347¹

Step-3: Factors of 5185

List of positive integer factors of 5185 that divides 5185 without a remainder.

1, 5, 17, 61, 85, 305, 1037

Step-4: Factors of 5205

List of positive integer factors of 5205 that divides 5185 without a remainder.

1, 3, 5, 15, 347, 1041, 1735

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5185 and 5205. The biggest common factor number is the GCF number.
So the greatest common factor 5185 and 5205 is 5.

Also check out the Least Common Multiple of 5185 and 5205