What is the Greatest Common Factor of 2065 and 2070?

Greatest common factor (GCF) of 2065 and 2070 is 5.

GCF(2065,2070) = 5

We will now calculate the prime factors of 2065 and 2070, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2065 and 2070.

How to find the GCF of 2065 and 2070?

We will first find the prime factorization of 2065 and 2070. After we will calculate the factors of 2065 and 2070 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 2070

Prime factors of 2070 are 2, 3, 5, 23. Prime factorization of 2070 in exponential form is:

2070 = 2¹ × 3² × 5¹ × 23¹

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 2070

List of positive integer factors of 2070 that divides 2065 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 23, 30, 45, 46, 69, 90, 115, 138, 207, 230, 345, 414, 690, 1035

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2065 and 2070. The biggest common factor number is the GCF number.
So the greatest common factor 2065 and 2070 is 5.

Also check out the Least Common Multiple of 2065 and 2070