What is the Greatest Common Factor of 30096 and 30105?

Greatest common factor (GCF) of 30096 and 30105 is 9.

GCF(30096,30105) = 9

We will now calculate the prime factors of 30096 and 30105, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30096 and 30105.

How to find the GCF of 30096 and 30105?

We will first find the prime factorization of 30096 and 30105. After we will calculate the factors of 30096 and 30105 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 30105

Prime factors of 30105 are 3, 5, 223. Prime factorization of 30105 in exponential form is:

30105 = 3³ × 5¹ × 223¹

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 30105

List of positive integer factors of 30105 that divides 30096 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135, 223, 669, 1115, 2007, 3345, 6021, 10035

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30096 and 30105. The biggest common factor number is the GCF number.
So the greatest common factor 30096 and 30105 is 9.

Also check out the Least Common Multiple of 30096 and 30105