What is the Greatest Common Factor of 30096 and 30112?

Greatest common factor (GCF) of 30096 and 30112 is 16.

GCF(30096,30112) = 16

We will now calculate the prime factors of 30096 and 30112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30096 and 30112.

How to find the GCF of 30096 and 30112?

We will first find the prime factorization of 30096 and 30112. After we will calculate the factors of 30096 and 30112 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30112

Prime factors of 30112 are 2, 941. Prime factorization of 30112 in exponential form is:

30112 = 2⁵ × 941¹

Step-3: Factors of 30096

List of positive integer factors of 30096 that divides 30096 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

Step-4: Factors of 30112

List of positive integer factors of 30112 that divides 30096 without a remainder.

1, 2, 4, 8, 16, 32, 941, 1882, 3764, 7528, 15056

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30096 and 30112. The biggest common factor number is the GCF number.
So the greatest common factor 30096 and 30112 is 16.

Also check out the Least Common Multiple of 30096 and 30112