What is the Greatest Common Factor of 1005 and 1009?

Greatest common factor (GCF) of 1005 and 1009 is 1.

GCF(1005,1009) = 1

We will now calculate the prime factors of 1005 and 1009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1005 and 1009.

How to find the GCF of 1005 and 1009?

We will first find the prime factorization of 1005 and 1009. After we will calculate the factors of 1005 and 1009 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 1009

Prime factors of 1009 are 1009. Prime factorization of 1009 in exponential form is:

1009 = 1009¹

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 1009

List of positive integer factors of 1009 that divides 1005 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1005 and 1009. The biggest common factor number is the GCF number.
So the greatest common factor 1005 and 1009 is 1.

Also check out the Least Common Multiple of 1005 and 1009