What is the Greatest Common Factor of 30102 and 30114?

Greatest common factor (GCF) of 30102 and 30114 is 6.

GCF(30102,30114) = 6

We will now calculate the prime factors of 30102 and 30114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30102 and 30114.

How to find the GCF of 30102 and 30114?

We will first find the prime factorization of 30102 and 30114. After we will calculate the factors of 30102 and 30114 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30114

Prime factors of 30114 are 2, 3, 7, 239. Prime factorization of 30114 in exponential form is:

30114 = 2¹ × 3² × 7¹ × 239¹

Step-3: Factors of 30102

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

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

Step-4: Factors of 30114

List of positive integer factors of 30114 that divides 30102 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 239, 478, 717, 1434, 1673, 2151, 3346, 4302, 5019, 10038, 15057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30102 and 30114. The biggest common factor number is the GCF number.
So the greatest common factor 30102 and 30114 is 6.

Also check out the Least Common Multiple of 30102 and 30114