What is the Greatest Common Factor of 5214 and 5229?

Greatest common factor (GCF) of 5214 and 5229 is 3.

GCF(5214,5229) = 3

We will now calculate the prime factors of 5214 and 5229, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5214 and 5229.

How to find the GCF of 5214 and 5229?

We will first find the prime factorization of 5214 and 5229. After we will calculate the factors of 5214 and 5229 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 5229

Prime factors of 5229 are 3, 7, 83. Prime factorization of 5229 in exponential form is:

5229 = 3² × 7¹ × 83¹

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 5229

List of positive integer factors of 5229 that divides 5214 without a remainder.

1, 3, 7, 9, 21, 63, 83, 249, 581, 747, 1743

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5214 and 5229. The biggest common factor number is the GCF number.
So the greatest common factor 5214 and 5229 is 3.

Also check out the Least Common Multiple of 5214 and 5229