What is the Greatest Common Factor of 55200 and 55216?

Greatest common factor (GCF) of 55200 and 55216 is 16.

GCF(55200,55216) = 16

We will now calculate the prime factors of 55200 and 55216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55200 and 55216.

How to find the GCF of 55200 and 55216?

We will first find the prime factorization of 55200 and 55216. After we will calculate the factors of 55200 and 55216 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 55216

Prime factors of 55216 are 2, 7, 17, 29. Prime factorization of 55216 in exponential form is:

55216 = 2⁴ × 7¹ × 17¹ × 29¹

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 55216

List of positive integer factors of 55216 that divides 55200 without a remainder.

1, 2, 4, 7, 8, 14, 16, 17, 28, 29, 34, 56, 58, 68, 112, 116, 119, 136, 203, 232, 238, 272, 406, 464, 476, 493, 812, 952, 986, 1624, 1904, 1972, 3248, 3451, 3944, 6902, 7888, 13804, 27608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55200 and 55216. The biggest common factor number is the GCF number.
So the greatest common factor 55200 and 55216 is 16.

Also check out the Least Common Multiple of 55200 and 55216