What is the Greatest Common Factor of 999 and 1005?

Greatest common factor (GCF) of 999 and 1005 is 3.

GCF(999,1005) = 3

We will now calculate the prime factors of 999 and 1005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 999 and 1005.

How to find the GCF of 999 and 1005?

We will first find the prime factorization of 999 and 1005. After we will calculate the factors of 999 and 1005 and find the biggest common factor number .

Step-1: Prime Factorization of 999

Prime factors of 999 are 3, 37. Prime factorization of 999 in exponential form is:

999 = 3³ × 37¹

Step-2: 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-3: Factors of 999

List of positive integer factors of 999 that divides 999 without a remainder.

1, 3, 9, 27, 37, 111, 333

Step-4: Factors of 1005

List of positive integer factors of 1005 that divides 999 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 999 and 1005. The biggest common factor number is the GCF number.
So the greatest common factor 999 and 1005 is 3.

Also check out the Least Common Multiple of 999 and 1005