What is the Greatest Common Factor of 5205 and 5214?

Greatest common factor (GCF) of 5205 and 5214 is 3.

GCF(5205,5214) = 3

We will now calculate the prime factors of 5205 and 5214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5205 and 5214.

How to find the GCF of 5205 and 5214?

We will first find the prime factorization of 5205 and 5214. After we will calculate the factors of 5205 and 5214 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 5214

Prime factors of 5214 are 2, 3, 11, 79. Prime factorization of 5214 in exponential form is:

5214 = 2¹ × 3¹ × 11¹ × 79¹

Step-3: Factors of 5205

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

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

Step-4: Factors of 5214

List of positive integer factors of 5214 that divides 5205 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 79, 158, 237, 474, 869, 1738, 2607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5205 and 5214. The biggest common factor number is the GCF number.
So the greatest common factor 5205 and 5214 is 3.

Also check out the Least Common Multiple of 5205 and 5214