What is the Greatest Common Factor of 65325 and 65338?

Greatest common factor (GCF) of 65325 and 65338 is 13.

GCF(65325,65338) = 13

We will now calculate the prime factors of 65325 and 65338, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65325 and 65338.

How to find the GCF of 65325 and 65338?

We will first find the prime factorization of 65325 and 65338. After we will calculate the factors of 65325 and 65338 and find the biggest common factor number .

Step-1: Prime Factorization of 65325

Prime factors of 65325 are 3, 5, 13, 67. Prime factorization of 65325 in exponential form is:

65325 = 3¹ × 5² × 13¹ × 67¹

Step-2: Prime Factorization of 65338

Prime factors of 65338 are 2, 7, 13, 359. Prime factorization of 65338 in exponential form is:

65338 = 2¹ × 7¹ × 13¹ × 359¹

Step-3: Factors of 65325

List of positive integer factors of 65325 that divides 65325 without a remainder.

1, 3, 5, 13, 15, 25, 39, 65, 67, 75, 195, 201, 325, 335, 871, 975, 1005, 1675, 2613, 4355, 5025, 13065, 21775

Step-4: Factors of 65338

List of positive integer factors of 65338 that divides 65325 without a remainder.

1, 2, 7, 13, 14, 26, 91, 182, 359, 718, 2513, 4667, 5026, 9334, 32669

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65325 and 65338. The biggest common factor number is the GCF number.
So the greatest common factor 65325 and 65338 is 13.

Also check out the Least Common Multiple of 65325 and 65338