What is the Greatest Common Factor of 55200 and 55209?

Greatest common factor (GCF) of 55200 and 55209 is 3.

GCF(55200,55209) = 3

We will now calculate the prime factors of 55200 and 55209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55200 and 55209.

How to find the GCF of 55200 and 55209?

We will first find the prime factorization of 55200 and 55209. After we will calculate the factors of 55200 and 55209 and find the biggest common factor number .

Step-1: Prime Factorization of 55200

Prime factors of 55200 are 2, 3, 5, 23. Prime factorization of 55200 in exponential form is:

55200 = 2⁵ × 3¹ × 5² × 23¹

Step-2: Prime Factorization of 55209

Prime factors of 55209 are 3, 7, 11, 239. Prime factorization of 55209 in exponential form is:

55209 = 3¹ × 7¹ × 11¹ × 239¹

Step-3: Factors of 55200

List of positive integer factors of 55200 that divides 55200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 23, 24, 25, 30, 32, 40, 46, 48, 50, 60, 69, 75, 80, 92, 96, 100, 115, 120, 138, 150, 160, 184, 200, 230, 240, 276, 300, 345, 368, 400, 460, 480, 552, 575, 600, 690, 736, 800, 920, 1104, 1150, 1200, 1380, 1725, 1840, 2208, 2300, 2400, 2760, 3450, 3680, 4600, 5520, 6900, 9200, 11040, 13800, 18400, 27600

Step-4: Factors of 55209

List of positive integer factors of 55209 that divides 55200 without a remainder.

1, 3, 7, 11, 21, 33, 77, 231, 239, 717, 1673, 2629, 5019, 7887, 18403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55200 and 55209. The biggest common factor number is the GCF number.
So the greatest common factor 55200 and 55209 is 3.

Also check out the Least Common Multiple of 55200 and 55209