What is the Greatest Common Factor of 30080 and 30096?

Greatest common factor (GCF) of 30080 and 30096 is 16.

GCF(30080,30096) = 16

We will now calculate the prime factors of 30080 and 30096, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30080 and 30096.

How to find the GCF of 30080 and 30096?

We will first find the prime factorization of 30080 and 30096. After we will calculate the factors of 30080 and 30096 and find the biggest common factor number .

Step-1: Prime Factorization of 30080

Prime factors of 30080 are 2, 5, 47. Prime factorization of 30080 in exponential form is:

30080 = 2⁷ × 5¹ × 47¹

Step-2: Prime Factorization of 30096

Prime factors of 30096 are 2, 3, 11, 19. Prime factorization of 30096 in exponential form is:

30096 = 2⁴ × 3² × 11¹ × 19¹

Step-3: Factors of 30080

List of positive integer factors of 30080 that divides 30080 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 47, 64, 80, 94, 128, 160, 188, 235, 320, 376, 470, 640, 752, 940, 1504, 1880, 3008, 3760, 6016, 7520, 15040

Step-4: Factors of 30096

List of positive integer factors of 30096 that divides 30080 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 19, 22, 24, 33, 36, 38, 44, 48, 57, 66, 72, 76, 88, 99, 114, 132, 144, 152, 171, 176, 198, 209, 228, 264, 304, 342, 396, 418, 456, 528, 627, 684, 792, 836, 912, 1254, 1368, 1584, 1672, 1881, 2508, 2736, 3344, 3762, 5016, 7524, 10032, 15048

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30080 and 30096. The biggest common factor number is the GCF number.
So the greatest common factor 30080 and 30096 is 16.

Also check out the Least Common Multiple of 30080 and 30096