What is the Greatest Common Factor of 30072 and 30084?

Greatest common factor (GCF) of 30072 and 30084 is 12.

GCF(30072,30084) = 12

We will now calculate the prime factors of 30072 and 30084, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30072 and 30084.

How to find the GCF of 30072 and 30084?

We will first find the prime factorization of 30072 and 30084. After we will calculate the factors of 30072 and 30084 and find the biggest common factor number .

Step-1: Prime Factorization of 30072

Prime factors of 30072 are 2, 3, 7, 179. Prime factorization of 30072 in exponential form is:

30072 = 2³ × 3¹ × 7¹ × 179¹

Step-2: 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-3: Factors of 30072

List of positive integer factors of 30072 that divides 30072 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168, 179, 358, 537, 716, 1074, 1253, 1432, 2148, 2506, 3759, 4296, 5012, 7518, 10024, 15036

Step-4: Factors of 30084

List of positive integer factors of 30084 that divides 30072 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30072 and 30084. The biggest common factor number is the GCF number.
So the greatest common factor 30072 and 30084 is 12.

Also check out the Least Common Multiple of 30072 and 30084