What is the Greatest Common Factor of 77200 and 77220?

Greatest common factor (GCF) of 77200 and 77220 is 20.

GCF(77200,77220) = 20

We will now calculate the prime factors of 77200 and 77220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77200 and 77220.

How to find the GCF of 77200 and 77220?

We will first find the prime factorization of 77200 and 77220. After we will calculate the factors of 77200 and 77220 and find the biggest common factor number .

Step-1: Prime Factorization of 77200

Prime factors of 77200 are 2, 5, 193. Prime factorization of 77200 in exponential form is:

77200 = 2⁴ × 5² × 193¹

Step-2: Prime Factorization of 77220

Prime factors of 77220 are 2, 3, 5, 11, 13. Prime factorization of 77220 in exponential form is:

77220 = 2² × 3³ × 5¹ × 11¹ × 13¹

Step-3: Factors of 77200

List of positive integer factors of 77200 that divides 77200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 193, 200, 386, 400, 772, 965, 1544, 1930, 3088, 3860, 4825, 7720, 9650, 15440, 19300, 38600

Step-4: Factors of 77220

List of positive integer factors of 77220 that divides 77200 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 15, 18, 20, 22, 26, 27, 30, 33, 36, 39, 44, 45, 52, 54, 55, 60, 65, 66, 78, 90, 99, 108, 110, 117, 130, 132, 135, 143, 156, 165, 180, 195, 198, 220, 234, 260, 270, 286, 297, 330, 351, 390, 396, 429, 468, 495, 540, 572, 585, 594, 660, 702, 715, 780, 858, 990, 1170, 1188, 1287, 1404, 1430, 1485, 1716, 1755, 1980, 2145, 2340, 2574, 2860, 2970, 3510, 3861, 4290, 5148, 5940, 6435, 7020, 7722, 8580, 12870, 15444, 19305, 25740, 38610

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77200 and 77220. The biggest common factor number is the GCF number.
So the greatest common factor 77200 and 77220 is 20.

Also check out the Least Common Multiple of 77200 and 77220