What is the Greatest Common Factor of 5214 and 5230?

Greatest common factor (GCF) of 5214 and 5230 is 2.

GCF(5214,5230) = 2

We will now calculate the prime factors of 5214 and 5230, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5214 and 5230.

How to find the GCF of 5214 and 5230?

We will first find the prime factorization of 5214 and 5230. After we will calculate the factors of 5214 and 5230 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 5230

Prime factors of 5230 are 2, 5, 523. Prime factorization of 5230 in exponential form is:

5230 = 2¹ × 5¹ × 523¹

Step-3: Factors of 5214

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

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

Step-4: Factors of 5230

List of positive integer factors of 5230 that divides 5214 without a remainder.

1, 2, 5, 10, 523, 1046, 2615

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5214 and 5230. The biggest common factor number is the GCF number.
So the greatest common factor 5214 and 5230 is 2.

Also check out the Least Common Multiple of 5214 and 5230