What is the Greatest Common Factor of 2065 and 2075?

Greatest common factor (GCF) of 2065 and 2075 is 5.

GCF(2065,2075) = 5

We will now calculate the prime factors of 2065 and 2075, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2065 and 2075.

How to find the GCF of 2065 and 2075?

We will first find the prime factorization of 2065 and 2075. After we will calculate the factors of 2065 and 2075 and find the biggest common factor number .

Step-1: Prime Factorization of 2065

Prime factors of 2065 are 5, 7, 59. Prime factorization of 2065 in exponential form is:

2065 = 5¹ × 7¹ × 59¹

Step-2: Prime Factorization of 2075

Prime factors of 2075 are 5, 83. Prime factorization of 2075 in exponential form is:

2075 = 5² × 83¹

Step-3: Factors of 2065

List of positive integer factors of 2065 that divides 2065 without a remainder.

1, 5, 7, 35, 59, 295, 413

Step-4: Factors of 2075

List of positive integer factors of 2075 that divides 2065 without a remainder.

1, 5, 25, 83, 415

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2065 and 2075. The biggest common factor number is the GCF number.
So the greatest common factor 2065 and 2075 is 5.

Also check out the Least Common Multiple of 2065 and 2075