What is the Greatest Common Factor of 1029 and 1038?

Greatest common factor (GCF) of 1029 and 1038 is 3.

GCF(1029,1038) = 3

We will now calculate the prime factors of 1029 and 1038, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1029 and 1038.

How to find the GCF of 1029 and 1038?

We will first find the prime factorization of 1029 and 1038. After we will calculate the factors of 1029 and 1038 and find the biggest common factor number .

Step-1: Prime Factorization of 1029

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

1029 = 3¹ × 7³

Step-2: Prime Factorization of 1038

Prime factors of 1038 are 2, 3, 173. Prime factorization of 1038 in exponential form is:

1038 = 2¹ × 3¹ × 173¹

Step-3: Factors of 1029

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

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

Step-4: Factors of 1038

List of positive integer factors of 1038 that divides 1029 without a remainder.

1, 2, 3, 6, 173, 346, 519

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1029 and 1038. The biggest common factor number is the GCF number.
So the greatest common factor 1029 and 1038 is 3.

Also check out the Least Common Multiple of 1029 and 1038