What is the Greatest Common Factor of 4199 and 4214?

Greatest common factor (GCF) of 4199 and 4214 is 1.

GCF(4199,4214) = 1

We will now calculate the prime factors of 4199 and 4214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4199 and 4214.

How to find the GCF of 4199 and 4214?

We will first find the prime factorization of 4199 and 4214. After we will calculate the factors of 4199 and 4214 and find the biggest common factor number .

Step-1: Prime Factorization of 4199

Prime factors of 4199 are 13, 17, 19. Prime factorization of 4199 in exponential form is:

4199 = 13¹ × 17¹ × 19¹

Step-2: Prime Factorization of 4214

Prime factors of 4214 are 2, 7, 43. Prime factorization of 4214 in exponential form is:

4214 = 2¹ × 7² × 43¹

Step-3: Factors of 4199

List of positive integer factors of 4199 that divides 4199 without a remainder.

1, 13, 17, 19, 221, 247, 323

Step-4: Factors of 4214

List of positive integer factors of 4214 that divides 4199 without a remainder.

1, 2, 7, 14, 43, 49, 86, 98, 301, 602, 2107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4199 and 4214. The biggest common factor number is the GCF number.
So the greatest common factor 4199 and 4214 is 1.

Also check out the Least Common Multiple of 4199 and 4214