What is the Greatest Common Factor of 34200 and 34219?

Greatest common factor (GCF) of 34200 and 34219 is 19.

GCF(34200,34219) = 19

We will now calculate the prime factors of 34200 and 34219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34200 and 34219.

How to find the GCF of 34200 and 34219?

We will first find the prime factorization of 34200 and 34219. After we will calculate the factors of 34200 and 34219 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 34219

Prime factors of 34219 are 19, 1801. Prime factorization of 34219 in exponential form is:

34219 = 19¹ × 1801¹

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 34219

List of positive integer factors of 34219 that divides 34200 without a remainder.

1, 19, 1801

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34200 and 34219. The biggest common factor number is the GCF number.
So the greatest common factor 34200 and 34219 is 19.

Also check out the Least Common Multiple of 34200 and 34219