What is the Greatest Common Factor of 5185 and 5202?

Greatest common factor (GCF) of 5185 and 5202 is 17.

GCF(5185,5202) = 17

We will now calculate the prime factors of 5185 and 5202, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5185 and 5202.

How to find the GCF of 5185 and 5202?

We will first find the prime factorization of 5185 and 5202. After we will calculate the factors of 5185 and 5202 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 5202

Prime factors of 5202 are 2, 3, 17. Prime factorization of 5202 in exponential form is:

5202 = 2¹ × 3² × 17²

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 5202

List of positive integer factors of 5202 that divides 5185 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 289, 306, 578, 867, 1734, 2601

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5185 and 5202. The biggest common factor number is the GCF number.
So the greatest common factor 5185 and 5202 is 17.

Also check out the Least Common Multiple of 5185 and 5202