What is the Greatest Common Factor of 1065 and 1074?

Greatest common factor (GCF) of 1065 and 1074 is 3.

GCF(1065,1074) = 3

We will now calculate the prime factors of 1065 and 1074, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1065 and 1074.

How to find the GCF of 1065 and 1074?

We will first find the prime factorization of 1065 and 1074. After we will calculate the factors of 1065 and 1074 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 1074

Prime factors of 1074 are 2, 3, 179. Prime factorization of 1074 in exponential form is:

1074 = 2¹ × 3¹ × 179¹

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 1074

List of positive integer factors of 1074 that divides 1065 without a remainder.

1, 2, 3, 6, 179, 358, 537

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1065 and 1074. The biggest common factor number is the GCF number.
So the greatest common factor 1065 and 1074 is 3.

Also check out the Least Common Multiple of 1065 and 1074