What is the Greatest Common Factor of 65002 and 65016?

Greatest common factor (GCF) of 65002 and 65016 is 14.

GCF(65002,65016) = 14

We will now calculate the prime factors of 65002 and 65016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65002 and 65016.

How to find the GCF of 65002 and 65016?

We will first find the prime factorization of 65002 and 65016. After we will calculate the factors of 65002 and 65016 and find the biggest common factor number .

Step-1: Prime Factorization of 65002

Prime factors of 65002 are 2, 7, 4643. Prime factorization of 65002 in exponential form is:

65002 = 2¹ × 7¹ × 4643¹

Step-2: Prime Factorization of 65016

Prime factors of 65016 are 2, 3, 7, 43. Prime factorization of 65016 in exponential form is:

65016 = 2³ × 3³ × 7¹ × 43¹

Step-3: Factors of 65002

List of positive integer factors of 65002 that divides 65002 without a remainder.

1, 2, 7, 14, 4643, 9286, 32501

Step-4: Factors of 65016

List of positive integer factors of 65016 that divides 65002 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 43, 54, 56, 63, 72, 84, 86, 108, 126, 129, 168, 172, 189, 216, 252, 258, 301, 344, 378, 387, 504, 516, 602, 756, 774, 903, 1032, 1161, 1204, 1512, 1548, 1806, 2322, 2408, 2709, 3096, 3612, 4644, 5418, 7224, 8127, 9288, 10836, 16254, 21672, 32508

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65002 and 65016. The biggest common factor number is the GCF number.
So the greatest common factor 65002 and 65016 is 14.

Also check out the Least Common Multiple of 65002 and 65016