What is the Greatest Common Factor of 1065 and 1080?

Greatest common factor (GCF) of 1065 and 1080 is 15.

GCF(1065,1080) = 15

We will now calculate the prime factors of 1065 and 1080, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1065 and 1080.

How to find the GCF of 1065 and 1080?

We will first find the prime factorization of 1065 and 1080. After we will calculate the factors of 1065 and 1080 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 1080

Prime factors of 1080 are 2, 3, 5. Prime factorization of 1080 in exponential form is:

1080 = 2³ × 3³ × 5¹

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 1080

List of positive integer factors of 1080 that divides 1065 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1065 and 1080. The biggest common factor number is the GCF number.
So the greatest common factor 1065 and 1080 is 15.

Also check out the Least Common Multiple of 1065 and 1080