What is the Greatest Common Factor of 65275 and 65289?

Greatest common factor (GCF) of 65275 and 65289 is 7.

GCF(65275,65289) = 7

We will now calculate the prime factors of 65275 and 65289, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65275 and 65289.

How to find the GCF of 65275 and 65289?

We will first find the prime factorization of 65275 and 65289. After we will calculate the factors of 65275 and 65289 and find the biggest common factor number .

Step-1: Prime Factorization of 65275

Prime factors of 65275 are 5, 7, 373. Prime factorization of 65275 in exponential form is:

65275 = 5² × 7¹ × 373¹

Step-2: Prime Factorization of 65289

Prime factors of 65289 are 3, 7, 3109. Prime factorization of 65289 in exponential form is:

65289 = 3¹ × 7¹ × 3109¹

Step-3: Factors of 65275

List of positive integer factors of 65275 that divides 65275 without a remainder.

1, 5, 7, 25, 35, 175, 373, 1865, 2611, 9325, 13055

Step-4: Factors of 65289

List of positive integer factors of 65289 that divides 65275 without a remainder.

1, 3, 7, 21, 3109, 9327, 21763

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65275 and 65289. The biggest common factor number is the GCF number.
So the greatest common factor 65275 and 65289 is 7.

Also check out the Least Common Multiple of 65275 and 65289