What is the Greatest Common Factor of 55200 and 55214?

Greatest common factor (GCF) of 55200 and 55214 is 2.

GCF(55200,55214) = 2

We will now calculate the prime factors of 55200 and 55214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55200 and 55214.

How to find the GCF of 55200 and 55214?

We will first find the prime factorization of 55200 and 55214. After we will calculate the factors of 55200 and 55214 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 55214

Prime factors of 55214 are 2, 19, 1453. Prime factorization of 55214 in exponential form is:

55214 = 2¹ × 19¹ × 1453¹

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 55214

List of positive integer factors of 55214 that divides 55200 without a remainder.

1, 2, 19, 38, 1453, 2906, 27607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55200 and 55214. The biggest common factor number is the GCF number.
So the greatest common factor 55200 and 55214 is 2.

Also check out the Least Common Multiple of 55200 and 55214