What is the Greatest Common Factor of 2002 and 2010?

Greatest common factor (GCF) of 2002 and 2010 is 2.

GCF(2002,2010) = 2

We will now calculate the prime factors of 2002 and 2010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2002 and 2010.

How to find the GCF of 2002 and 2010?

We will first find the prime factorization of 2002 and 2010. After we will calculate the factors of 2002 and 2010 and find the biggest common factor number .

Step-1: Prime Factorization of 2002

Prime factors of 2002 are 2, 7, 11, 13. Prime factorization of 2002 in exponential form is:

2002 = 2¹ × 7¹ × 11¹ × 13¹

Step-2: Prime Factorization of 2010

Prime factors of 2010 are 2, 3, 5, 67. Prime factorization of 2010 in exponential form is:

2010 = 2¹ × 3¹ × 5¹ × 67¹

Step-3: Factors of 2002

List of positive integer factors of 2002 that divides 2002 without a remainder.

1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001

Step-4: Factors of 2010

List of positive integer factors of 2010 that divides 2002 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2002 and 2010. The biggest common factor number is the GCF number.
So the greatest common factor 2002 and 2010 is 2.

Also check out the Least Common Multiple of 2002 and 2010