What is the Greatest Common Factor of 30005 and 30012?

Greatest common factor (GCF) of 30005 and 30012 is 1.

GCF(30005,30012) = 1

We will now calculate the prime factors of 30005 and 30012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30005 and 30012.

How to find the GCF of 30005 and 30012?

We will first find the prime factorization of 30005 and 30012. After we will calculate the factors of 30005 and 30012 and find the biggest common factor number .

Step-1: Prime Factorization of 30005

Prime factors of 30005 are 5, 17, 353. Prime factorization of 30005 in exponential form is:

30005 = 5¹ × 17¹ × 353¹

Step-2: Prime Factorization of 30012

Prime factors of 30012 are 2, 3, 41, 61. Prime factorization of 30012 in exponential form is:

30012 = 2² × 3¹ × 41¹ × 61¹

Step-3: Factors of 30005

List of positive integer factors of 30005 that divides 30005 without a remainder.

1, 5, 17, 85, 353, 1765, 6001

Step-4: Factors of 30012

List of positive integer factors of 30012 that divides 30005 without a remainder.

1, 2, 3, 4, 6, 12, 41, 61, 82, 122, 123, 164, 183, 244, 246, 366, 492, 732, 2501, 5002, 7503, 10004, 15006

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30005 and 30012. The biggest common factor number is the GCF number.
So the greatest common factor 30005 and 30012 is 1.

Also check out the Least Common Multiple of 30005 and 30012