What is the Greatest Common Factor of 35200 and 35209?

Greatest common factor (GCF) of 35200 and 35209 is 1.

GCF(35200,35209) = 1

We will now calculate the prime factors of 35200 and 35209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35200 and 35209.

How to find the GCF of 35200 and 35209?

We will first find the prime factorization of 35200 and 35209. After we will calculate the factors of 35200 and 35209 and find the biggest common factor number .

Step-1: Prime Factorization of 35200

Prime factors of 35200 are 2, 5, 11. Prime factorization of 35200 in exponential form is:

35200 = 2⁷ × 5² × 11¹

Step-2: Prime Factorization of 35209

Prime factors of 35209 are 137, 257. Prime factorization of 35209 in exponential form is:

35209 = 137¹ × 257¹

Step-3: Factors of 35200

List of positive integer factors of 35200 that divides 35200 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 32, 40, 44, 50, 55, 64, 80, 88, 100, 110, 128, 160, 176, 200, 220, 275, 320, 352, 400, 440, 550, 640, 704, 800, 880, 1100, 1408, 1600, 1760, 2200, 3200, 3520, 4400, 7040, 8800, 17600

Step-4: Factors of 35209

List of positive integer factors of 35209 that divides 35200 without a remainder.

1, 137, 257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35200 and 35209. The biggest common factor number is the GCF number.
So the greatest common factor 35200 and 35209 is 1.

Also check out the Least Common Multiple of 35200 and 35209