What is the Greatest Common Factor of 1005 and 1012?

Greatest common factor (GCF) of 1005 and 1012 is 1.

GCF(1005,1012) = 1

We will now calculate the prime factors of 1005 and 1012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1005 and 1012.

How to find the GCF of 1005 and 1012?

We will first find the prime factorization of 1005 and 1012. After we will calculate the factors of 1005 and 1012 and find the biggest common factor number .

Step-1: Prime Factorization of 1005

Prime factors of 1005 are 3, 5, 67. Prime factorization of 1005 in exponential form is:

1005 = 3¹ × 5¹ × 67¹

Step-2: Prime Factorization of 1012

Prime factors of 1012 are 2, 11, 23. Prime factorization of 1012 in exponential form is:

1012 = 2² × 11¹ × 23¹

Step-3: Factors of 1005

List of positive integer factors of 1005 that divides 1005 without a remainder.

1, 3, 5, 15, 67, 201, 335

Step-4: Factors of 1012

List of positive integer factors of 1012 that divides 1005 without a remainder.

1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1005 and 1012. The biggest common factor number is the GCF number.
So the greatest common factor 1005 and 1012 is 1.

Also check out the Least Common Multiple of 1005 and 1012