What is the Greatest Common Factor of 27720 and 27730?

Greatest common factor (GCF) of 27720 and 27730 is 10.

GCF(27720,27730) = 10

We will now calculate the prime factors of 27720 and 27730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27720 and 27730.

How to find the GCF of 27720 and 27730?

We will first find the prime factorization of 27720 and 27730. After we will calculate the factors of 27720 and 27730 and find the biggest common factor number .

Step-1: Prime Factorization of 27720

Prime factors of 27720 are 2, 3, 5, 7, 11. Prime factorization of 27720 in exponential form is:

27720 = 2³ × 3² × 5¹ × 7¹ × 11¹

Step-2: Prime Factorization of 27730

Prime factors of 27730 are 2, 5, 47, 59. Prime factorization of 27730 in exponential form is:

27730 = 2¹ × 5¹ × 47¹ × 59¹

Step-3: Factors of 27720

List of positive integer factors of 27720 that divides 27720 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 24, 28, 30, 33, 35, 36, 40, 42, 44, 45, 55, 56, 60, 63, 66, 70, 72, 77, 84, 88, 90, 99, 105, 110, 120, 126, 132, 140, 154, 165, 168, 180, 198, 210, 220, 231, 252, 264, 280, 308, 315, 330, 360, 385, 396, 420, 440, 462, 495, 504, 616, 630, 660, 693, 770, 792, 840, 924, 990, 1155, 1260, 1320, 1386, 1540, 1848, 1980, 2310, 2520, 2772, 3080, 3465, 3960, 4620, 5544, 6930, 9240, 13860

Step-4: Factors of 27730

List of positive integer factors of 27730 that divides 27720 without a remainder.

1, 2, 5, 10, 47, 59, 94, 118, 235, 295, 470, 590, 2773, 5546, 13865

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27720 and 27730. The biggest common factor number is the GCF number.
So the greatest common factor 27720 and 27730 is 10.

Also check out the Least Common Multiple of 27720 and 27730