What is the Greatest Common Factor of 1065 and 1072?

Greatest common factor (GCF) of 1065 and 1072 is 1.

GCF(1065,1072) = 1

We will now calculate the prime factors of 1065 and 1072, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1065 and 1072.

How to find the GCF of 1065 and 1072?

We will first find the prime factorization of 1065 and 1072. After we will calculate the factors of 1065 and 1072 and find the biggest common factor number .

Step-1: Prime Factorization of 1065

Prime factors of 1065 are 3, 5, 71. Prime factorization of 1065 in exponential form is:

1065 = 3¹ × 5¹ × 71¹

Step-2: Prime Factorization of 1072

Prime factors of 1072 are 2, 67. Prime factorization of 1072 in exponential form is:

1072 = 2⁴ × 67¹

Step-3: Factors of 1065

List of positive integer factors of 1065 that divides 1065 without a remainder.

1, 3, 5, 15, 71, 213, 355

Step-4: Factors of 1072

List of positive integer factors of 1072 that divides 1065 without a remainder.

1, 2, 4, 8, 16, 67, 134, 268, 536

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1065 and 1072. The biggest common factor number is the GCF number.
So the greatest common factor 1065 and 1072 is 1.

Also check out the Least Common Multiple of 1065 and 1072