What is the Greatest Common Factor of 27709 and 27720?

Greatest common factor (GCF) of 27709 and 27720 is 11.

GCF(27709,27720) = 11

We will now calculate the prime factors of 27709 and 27720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27709 and 27720.

How to find the GCF of 27709 and 27720?

We will first find the prime factorization of 27709 and 27720. After we will calculate the factors of 27709 and 27720 and find the biggest common factor number .

Step-1: Prime Factorization of 27709

Prime factors of 27709 are 11, 229. Prime factorization of 27709 in exponential form is:

27709 = 11² × 229¹

Step-2: 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-3: Factors of 27709

List of positive integer factors of 27709 that divides 27709 without a remainder.

1, 11, 121, 229, 2519

Step-4: Factors of 27720

List of positive integer factors of 27720 that divides 27709 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27709 and 27720. The biggest common factor number is the GCF number.
So the greatest common factor 27709 and 27720 is 11.

Also check out the Least Common Multiple of 27709 and 27720