What is the Greatest Common Factor of 34200 and 34214?

Greatest common factor (GCF) of 34200 and 34214 is 2.

GCF(34200,34214) = 2

We will now calculate the prime factors of 34200 and 34214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34200 and 34214.

How to find the GCF of 34200 and 34214?

We will first find the prime factorization of 34200 and 34214. After we will calculate the factors of 34200 and 34214 and find the biggest common factor number .

Step-1: Prime Factorization of 34200

Prime factors of 34200 are 2, 3, 5, 19. Prime factorization of 34200 in exponential form is:

34200 = 2³ × 3² × 5² × 19¹

Step-2: Prime Factorization of 34214

Prime factors of 34214 are 2, 17107. Prime factorization of 34214 in exponential form is:

34214 = 2¹ × 17107¹

Step-3: Factors of 34200

List of positive integer factors of 34200 that divides 34200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 25, 30, 36, 38, 40, 45, 50, 57, 60, 72, 75, 76, 90, 95, 100, 114, 120, 150, 152, 171, 180, 190, 200, 225, 228, 285, 300, 342, 360, 380, 450, 456, 475, 570, 600, 684, 760, 855, 900, 950, 1140, 1368, 1425, 1710, 1800, 1900, 2280, 2850, 3420, 3800, 4275, 5700, 6840, 8550, 11400, 17100

Step-4: Factors of 34214

List of positive integer factors of 34214 that divides 34200 without a remainder.

1, 2, 17107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34200 and 34214. The biggest common factor number is the GCF number.
So the greatest common factor 34200 and 34214 is 2.

Also check out the Least Common Multiple of 34200 and 34214