What is the Greatest Common Factor of 30105 and 30123?

Greatest common factor (GCF) of 30105 and 30123 is 9.

GCF(30105,30123) = 9

We will now calculate the prime factors of 30105 and 30123, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30105 and 30123.

How to find the GCF of 30105 and 30123?

We will first find the prime factorization of 30105 and 30123. After we will calculate the factors of 30105 and 30123 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 30123

Prime factors of 30123 are 3, 3347. Prime factorization of 30123 in exponential form is:

30123 = 3² × 3347¹

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 30123

List of positive integer factors of 30123 that divides 30105 without a remainder.

1, 3, 9, 3347, 10041

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30105 and 30123. The biggest common factor number is the GCF number.
So the greatest common factor 30105 and 30123 is 9.

Also check out the Least Common Multiple of 30105 and 30123