What is the Greatest Common Factor of 30720 and 30740?

Greatest common factor (GCF) of 30720 and 30740 is 20.

GCF(30720,30740) = 20

We will now calculate the prime factors of 30720 and 30740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30720 and 30740.

How to find the GCF of 30720 and 30740?

We will first find the prime factorization of 30720 and 30740. After we will calculate the factors of 30720 and 30740 and find the biggest common factor number .

Step-1: Prime Factorization of 30720

Prime factors of 30720 are 2, 3, 5. Prime factorization of 30720 in exponential form is:

30720 = 2¹¹ × 3¹ × 5¹

Step-2: Prime Factorization of 30740

Prime factors of 30740 are 2, 5, 29, 53. Prime factorization of 30740 in exponential form is:

30740 = 2² × 5¹ × 29¹ × 53¹

Step-3: Factors of 30720

List of positive integer factors of 30720 that divides 30720 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2048, 2560, 3072, 3840, 5120, 6144, 7680, 10240, 15360

Step-4: Factors of 30740

List of positive integer factors of 30740 that divides 30720 without a remainder.

1, 2, 4, 5, 10, 20, 29, 53, 58, 106, 116, 145, 212, 265, 290, 530, 580, 1060, 1537, 3074, 6148, 7685, 15370

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30720 and 30740. The biggest common factor number is the GCF number.
So the greatest common factor 30720 and 30740 is 20.

Also check out the Least Common Multiple of 30720 and 30740