What is the Greatest Common Factor of 55180 and 55200?

Greatest common factor (GCF) of 55180 and 55200 is 20.

GCF(55180,55200) = 20

We will now calculate the prime factors of 55180 and 55200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55180 and 55200.

How to find the GCF of 55180 and 55200?

We will first find the prime factorization of 55180 and 55200. After we will calculate the factors of 55180 and 55200 and find the biggest common factor number .

Step-1: Prime Factorization of 55180

Prime factors of 55180 are 2, 5, 31, 89. Prime factorization of 55180 in exponential form is:

55180 = 2² × 5¹ × 31¹ × 89¹

Step-2: 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-3: Factors of 55180

List of positive integer factors of 55180 that divides 55180 without a remainder.

1, 2, 4, 5, 10, 20, 31, 62, 89, 124, 155, 178, 310, 356, 445, 620, 890, 1780, 2759, 5518, 11036, 13795, 27590

Step-4: Factors of 55200

List of positive integer factors of 55200 that divides 55180 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55180 and 55200. The biggest common factor number is the GCF number.
So the greatest common factor 55180 and 55200 is 20.

Also check out the Least Common Multiple of 55180 and 55200