What is the Greatest Common Factor of 12005 and 12012?

Greatest common factor (GCF) of 12005 and 12012 is 7.

GCF(12005,12012) = 7

We will now calculate the prime factors of 12005 and 12012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12005 and 12012.

How to find the GCF of 12005 and 12012?

We will first find the prime factorization of 12005 and 12012. After we will calculate the factors of 12005 and 12012 and find the biggest common factor number .

Step-1: Prime Factorization of 12005

Prime factors of 12005 are 5, 7. Prime factorization of 12005 in exponential form is:

12005 = 5¹ × 7⁴

Step-2: Prime Factorization of 12012

Prime factors of 12012 are 2, 3, 7, 11, 13. Prime factorization of 12012 in exponential form is:

12012 = 2² × 3¹ × 7¹ × 11¹ × 13¹

Step-3: Factors of 12005

List of positive integer factors of 12005 that divides 12005 without a remainder.

1, 5, 7, 35, 49, 245, 343, 1715, 2401

Step-4: Factors of 12012

List of positive integer factors of 12012 that divides 12005 without a remainder.

1, 2, 3, 4, 6, 7, 11, 12, 13, 14, 21, 22, 26, 28, 33, 39, 42, 44, 52, 66, 77, 78, 84, 91, 132, 143, 154, 156, 182, 231, 273, 286, 308, 364, 429, 462, 546, 572, 858, 924, 1001, 1092, 1716, 2002, 3003, 4004, 6006

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12005 and 12012. The biggest common factor number is the GCF number.
So the greatest common factor 12005 and 12012 is 7.

Also check out the Least Common Multiple of 12005 and 12012