What is the Greatest Common Factor of 2012 and 2030?

Greatest common factor (GCF) of 2012 and 2030 is 2.

GCF(2012,2030) = 2

We will now calculate the prime factors of 2012 and 2030, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2012 and 2030.

How to find the GCF of 2012 and 2030?

We will first find the prime factorization of 2012 and 2030. After we will calculate the factors of 2012 and 2030 and find the biggest common factor number .

Step-1: Prime Factorization of 2012

Prime factors of 2012 are 2, 503. Prime factorization of 2012 in exponential form is:

2012 = 2² × 503¹

Step-2: Prime Factorization of 2030

Prime factors of 2030 are 2, 5, 7, 29. Prime factorization of 2030 in exponential form is:

2030 = 2¹ × 5¹ × 7¹ × 29¹

Step-3: Factors of 2012

List of positive integer factors of 2012 that divides 2012 without a remainder.

1, 2, 4, 503, 1006

Step-4: Factors of 2030

List of positive integer factors of 2030 that divides 2012 without a remainder.

1, 2, 5, 7, 10, 14, 29, 35, 58, 70, 145, 203, 290, 406, 1015

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2012 and 2030. The biggest common factor number is the GCF number.
So the greatest common factor 2012 and 2030 is 2.

Also check out the Least Common Multiple of 2012 and 2030