What is the Greatest Common Factor of 30084 and 30096?

Greatest common factor (GCF) of 30084 and 30096 is 12.

GCF(30084,30096) = 12

We will now calculate the prime factors of 30084 and 30096, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30084 and 30096.

How to find the GCF of 30084 and 30096?

We will first find the prime factorization of 30084 and 30096. After we will calculate the factors of 30084 and 30096 and find the biggest common factor number .

Step-1: Prime Factorization of 30084

Prime factors of 30084 are 2, 3, 23, 109. Prime factorization of 30084 in exponential form is:

30084 = 2² × 3¹ × 23¹ × 109¹

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 30084

List of positive integer factors of 30084 that divides 30084 without a remainder.

1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 109, 138, 218, 276, 327, 436, 654, 1308, 2507, 5014, 7521, 10028, 15042

Step-4: Factors of 30096

List of positive integer factors of 30096 that divides 30084 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 30084 and 30096. The biggest common factor number is the GCF number.
So the greatest common factor 30084 and 30096 is 12.

Also check out the Least Common Multiple of 30084 and 30096