What is the Greatest Common Factor of 30105 and 30114?

Greatest common factor (GCF) of 30105 and 30114 is 9.

GCF(30105,30114) = 9

We will now calculate the prime factors of 30105 and 30114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30105 and 30114.

How to find the GCF of 30105 and 30114?

We will first find the prime factorization of 30105 and 30114. After we will calculate the factors of 30105 and 30114 and find the biggest common factor number .

Step-1: 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-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 30105

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

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

Step-4: Factors of 30114

List of positive integer factors of 30114 that divides 30105 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 30105 and 30114. The biggest common factor number is the GCF number.
So the greatest common factor 30105 and 30114 is 9.

Also check out the Least Common Multiple of 30105 and 30114