What is the Greatest Common Factor of 27720 and 27734?

Greatest common factor (GCF) of 27720 and 27734 is 14.

GCF(27720,27734) = 14

We will now calculate the prime factors of 27720 and 27734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27720 and 27734.

How to find the GCF of 27720 and 27734?

We will first find the prime factorization of 27720 and 27734. After we will calculate the factors of 27720 and 27734 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 27734

Prime factors of 27734 are 2, 7, 283. Prime factorization of 27734 in exponential form is:

27734 = 2¹ × 7² × 283¹

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 27734

List of positive integer factors of 27734 that divides 27720 without a remainder.

1, 2, 7, 14, 49, 98, 283, 566, 1981, 3962, 13867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27720 and 27734. The biggest common factor number is the GCF number.
So the greatest common factor 27720 and 27734 is 14.

Also check out the Least Common Multiple of 27720 and 27734