What is the Greatest Common Factor of 30084 and 30102?

Greatest common factor (GCF) of 30084 and 30102 is 6.

GCF(30084,30102) = 6

We will now calculate the prime factors of 30084 and 30102, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30084 and 30102.

How to find the GCF of 30084 and 30102?

We will first find the prime factorization of 30084 and 30102. After we will calculate the factors of 30084 and 30102 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 30102

Prime factors of 30102 are 2, 3, 29, 173. Prime factorization of 30102 in exponential form is:

30102 = 2¹ × 3¹ × 29¹ × 173¹

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 30102

List of positive integer factors of 30102 that divides 30084 without a remainder.

1, 2, 3, 6, 29, 58, 87, 173, 174, 346, 519, 1038, 5017, 10034, 15051

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30084 and 30102. The biggest common factor number is the GCF number.
So the greatest common factor 30084 and 30102 is 6.

Also check out the Least Common Multiple of 30084 and 30102