What is the Greatest Common Factor of 54720 and 54738?

Greatest common factor (GCF) of 54720 and 54738 is 18.

GCF(54720,54738) = 18

We will now calculate the prime factors of 54720 and 54738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54720 and 54738.

How to find the GCF of 54720 and 54738?

We will first find the prime factorization of 54720 and 54738. After we will calculate the factors of 54720 and 54738 and find the biggest common factor number .

Step-1: Prime Factorization of 54720

Prime factors of 54720 are 2, 3, 5, 19. Prime factorization of 54720 in exponential form is:

54720 = 2⁶ × 3² × 5¹ × 19¹

Step-2: Prime Factorization of 54738

Prime factors of 54738 are 2, 3, 3041. Prime factorization of 54738 in exponential form is:

54738 = 2¹ × 3² × 3041¹

Step-3: Factors of 54720

List of positive integer factors of 54720 that divides 54720 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24, 30, 32, 36, 38, 40, 45, 48, 57, 60, 64, 72, 76, 80, 90, 95, 96, 114, 120, 144, 152, 160, 171, 180, 190, 192, 228, 240, 285, 288, 304, 320, 342, 360, 380, 456, 480, 570, 576, 608, 684, 720, 760, 855, 912, 960, 1140, 1216, 1368, 1440, 1520, 1710, 1824, 2280, 2736, 2880, 3040, 3420, 3648, 4560, 5472, 6080, 6840, 9120, 10944, 13680, 18240, 27360

Step-4: Factors of 54738

List of positive integer factors of 54738 that divides 54720 without a remainder.

1, 2, 3, 6, 9, 18, 3041, 6082, 9123, 18246, 27369

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54720 and 54738. The biggest common factor number is the GCF number.
So the greatest common factor 54720 and 54738 is 18.

Also check out the Least Common Multiple of 54720 and 54738