What is the Greatest Common Factor of 1029 and 1035?

Greatest common factor (GCF) of 1029 and 1035 is 3.

GCF(1029,1035) = 3

We will now calculate the prime factors of 1029 and 1035, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1029 and 1035.

How to find the GCF of 1029 and 1035?

We will first find the prime factorization of 1029 and 1035. After we will calculate the factors of 1029 and 1035 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 1035

Prime factors of 1035 are 3, 5, 23. Prime factorization of 1035 in exponential form is:

1035 = 3² × 5¹ × 23¹

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 1035

List of positive integer factors of 1035 that divides 1029 without a remainder.

1, 3, 5, 9, 15, 23, 45, 69, 115, 207, 345

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1029 and 1035. The biggest common factor number is the GCF number.
So the greatest common factor 1029 and 1035 is 3.

Also check out the Least Common Multiple of 1029 and 1035