What is the Greatest Common Factor of 1005 and 1023?

Greatest common factor (GCF) of 1005 and 1023 is 3.

GCF(1005,1023) = 3

We will now calculate the prime factors of 1005 and 1023, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1005 and 1023.

How to find the GCF of 1005 and 1023?

We will first find the prime factorization of 1005 and 1023. After we will calculate the factors of 1005 and 1023 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 1023

Prime factors of 1023 are 3, 11, 31. Prime factorization of 1023 in exponential form is:

1023 = 3¹ × 11¹ × 31¹

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 1023

List of positive integer factors of 1023 that divides 1005 without a remainder.

1, 3, 11, 31, 33, 93, 341

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1005 and 1023. The biggest common factor number is the GCF number.
So the greatest common factor 1005 and 1023 is 3.

Also check out the Least Common Multiple of 1005 and 1023