What is the Greatest Common Factor of 1029 and 1036?

Greatest common factor (GCF) of 1029 and 1036 is 7.

GCF(1029,1036) = 7

We will now calculate the prime factors of 1029 and 1036, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1029 and 1036.

How to find the GCF of 1029 and 1036?

We will first find the prime factorization of 1029 and 1036. After we will calculate the factors of 1029 and 1036 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 1036

Prime factors of 1036 are 2, 7, 37. Prime factorization of 1036 in exponential form is:

1036 = 2² × 7¹ × 37¹

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 1036

List of positive integer factors of 1036 that divides 1029 without a remainder.

1, 2, 4, 7, 14, 28, 37, 74, 148, 259, 518

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1029 and 1036. The biggest common factor number is the GCF number.
So the greatest common factor 1029 and 1036 is 7.

Also check out the Least Common Multiple of 1029 and 1036