What is the Greatest Common Factor of 53199 and 53214?

Greatest common factor (GCF) of 53199 and 53214 is 3.

GCF(53199,53214) = 3

We will now calculate the prime factors of 53199 and 53214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53199 and 53214.

How to find the GCF of 53199 and 53214?

We will first find the prime factorization of 53199 and 53214. After we will calculate the factors of 53199 and 53214 and find the biggest common factor number .

Step-1: Prime Factorization of 53199

Prime factors of 53199 are 3, 23, 257. Prime factorization of 53199 in exponential form is:

53199 = 3² × 23¹ × 257¹

Step-2: Prime Factorization of 53214

Prime factors of 53214 are 2, 3, 7, 181. Prime factorization of 53214 in exponential form is:

53214 = 2¹ × 3¹ × 7² × 181¹

Step-3: Factors of 53199

List of positive integer factors of 53199 that divides 53199 without a remainder.

1, 3, 9, 23, 69, 207, 257, 771, 2313, 5911, 17733

Step-4: Factors of 53214

List of positive integer factors of 53214 that divides 53199 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 181, 294, 362, 543, 1086, 1267, 2534, 3801, 7602, 8869, 17738, 26607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53199 and 53214. The biggest common factor number is the GCF number.
So the greatest common factor 53199 and 53214 is 3.

Also check out the Least Common Multiple of 53199 and 53214