What is the Greatest Common Factor of 27720 and 27738?

Greatest common factor (GCF) of 27720 and 27738 is 18.

GCF(27720,27738) = 18

We will now calculate the prime factors of 27720 and 27738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27720 and 27738.

How to find the GCF of 27720 and 27738?

We will first find the prime factorization of 27720 and 27738. After we will calculate the factors of 27720 and 27738 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 27738

Prime factors of 27738 are 2, 3, 23, 67. Prime factorization of 27738 in exponential form is:

27738 = 2¹ × 3² × 23¹ × 67¹

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 27738

List of positive integer factors of 27738 that divides 27720 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 67, 69, 134, 138, 201, 207, 402, 414, 603, 1206, 1541, 3082, 4623, 9246, 13869

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27720 and 27738. The biggest common factor number is the GCF number.
So the greatest common factor 27720 and 27738 is 18.

Also check out the Least Common Multiple of 27720 and 27738