What is the Greatest Common Factor of 1004 and 1022?

Greatest common factor (GCF) of 1004 and 1022 is 2.

GCF(1004,1022) = 2

We will now calculate the prime factors of 1004 and 1022, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1004 and 1022.

How to find the GCF of 1004 and 1022?

We will first find the prime factorization of 1004 and 1022. After we will calculate the factors of 1004 and 1022 and find the biggest common factor number .

Step-1: Prime Factorization of 1004

Prime factors of 1004 are 2, 251. Prime factorization of 1004 in exponential form is:

1004 = 2² × 251¹

Step-2: Prime Factorization of 1022

Prime factors of 1022 are 2, 7, 73. Prime factorization of 1022 in exponential form is:

1022 = 2¹ × 7¹ × 73¹

Step-3: Factors of 1004

List of positive integer factors of 1004 that divides 1004 without a remainder.

1, 2, 4, 251, 502

Step-4: Factors of 1022

List of positive integer factors of 1022 that divides 1004 without a remainder.

1, 2, 7, 14, 73, 146, 511

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1004 and 1022. The biggest common factor number is the GCF number.
So the greatest common factor 1004 and 1022 is 2.

Also check out the Least Common Multiple of 1004 and 1022