What is the Greatest Common Factor of 1008 and 1022?

Greatest common factor (GCF) of 1008 and 1022 is 14.

GCF(1008,1022) = 14

We will now calculate the prime factors of 1008 and 1022, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1008 and 1022.

How to find the GCF of 1008 and 1022?

We will first find the prime factorization of 1008 and 1022. After we will calculate the factors of 1008 and 1022 and find the biggest common factor number .

Step-1: Prime Factorization of 1008

Prime factors of 1008 are 2, 3, 7. Prime factorization of 1008 in exponential form is:

1008 = 2⁴ × 3² × 7¹

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 1008

List of positive integer factors of 1008 that divides 1008 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504

Step-4: Factors of 1022

List of positive integer factors of 1022 that divides 1008 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1008 and 1022. The biggest common factor number is the GCF number.
So the greatest common factor 1008 and 1022 is 14.

Also check out the Least Common Multiple of 1008 and 1022