What is the Greatest Common Factor of 1022 and 1029?

Greatest common factor (GCF) of 1022 and 1029 is 7.

GCF(1022,1029) = 7

We will now calculate the prime factors of 1022 and 1029, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1022 and 1029.

How to find the GCF of 1022 and 1029?

We will first find the prime factorization of 1022 and 1029. After we will calculate the factors of 1022 and 1029 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1029

Prime factors of 1029 are 3, 7. Prime factorization of 1029 in exponential form is:

1029 = 3¹ × 7³

Step-3: Factors of 1022

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

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

Step-4: Factors of 1029

List of positive integer factors of 1029 that divides 1022 without a remainder.

1, 3, 7, 21, 49, 147, 343

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1022 and 1029. The biggest common factor number is the GCF number.
So the greatest common factor 1022 and 1029 is 7.

Also check out the Least Common Multiple of 1022 and 1029