What is the Greatest Common Factor of 30720 and 30728?

Greatest common factor (GCF) of 30720 and 30728 is 8.

GCF(30720,30728) = 8

We will now calculate the prime factors of 30720 and 30728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30720 and 30728.

How to find the GCF of 30720 and 30728?

We will first find the prime factorization of 30720 and 30728. After we will calculate the factors of 30720 and 30728 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 30728

Prime factors of 30728 are 2, 23, 167. Prime factorization of 30728 in exponential form is:

30728 = 2³ × 23¹ × 167¹

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 30728

List of positive integer factors of 30728 that divides 30720 without a remainder.

1, 2, 4, 8, 23, 46, 92, 167, 184, 334, 668, 1336, 3841, 7682, 15364

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30720 and 30728. The biggest common factor number is the GCF number.
So the greatest common factor 30720 and 30728 is 8.

Also check out the Least Common Multiple of 30720 and 30728