What is the Greatest Common Factor of 65875 and 65892?

Greatest common factor (GCF) of 65875 and 65892 is 17.

GCF(65875,65892) = 17

We will now calculate the prime factors of 65875 and 65892, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65875 and 65892.

How to find the GCF of 65875 and 65892?

We will first find the prime factorization of 65875 and 65892. After we will calculate the factors of 65875 and 65892 and find the biggest common factor number .

Step-1: Prime Factorization of 65875

Prime factors of 65875 are 5, 17, 31. Prime factorization of 65875 in exponential form is:

65875 = 5³ × 17¹ × 31¹

Step-2: Prime Factorization of 65892

Prime factors of 65892 are 2, 3, 17, 19. Prime factorization of 65892 in exponential form is:

65892 = 2² × 3¹ × 17² × 19¹

Step-3: Factors of 65875

List of positive integer factors of 65875 that divides 65875 without a remainder.

1, 5, 17, 25, 31, 85, 125, 155, 425, 527, 775, 2125, 2635, 3875, 13175

Step-4: Factors of 65892

List of positive integer factors of 65892 that divides 65875 without a remainder.

1, 2, 3, 4, 6, 12, 17, 19, 34, 38, 51, 57, 68, 76, 102, 114, 204, 228, 289, 323, 578, 646, 867, 969, 1156, 1292, 1734, 1938, 3468, 3876, 5491, 10982, 16473, 21964, 32946

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65875 and 65892. The biggest common factor number is the GCF number.
So the greatest common factor 65875 and 65892 is 17.

Also check out the Least Common Multiple of 65875 and 65892