What is the Greatest Common Factor of 68000 and 68017?

Greatest common factor (GCF) of 68000 and 68017 is 17.

GCF(68000,68017) = 17

We will now calculate the prime factors of 68000 and 68017, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 68000 and 68017.

How to find the GCF of 68000 and 68017?

We will first find the prime factorization of 68000 and 68017. After we will calculate the factors of 68000 and 68017 and find the biggest common factor number .

Step-1: Prime Factorization of 68000

Prime factors of 68000 are 2, 5, 17. Prime factorization of 68000 in exponential form is:

68000 = 2⁵ × 5³ × 17¹

Step-2: Prime Factorization of 68017

Prime factors of 68017 are 17, 4001. Prime factorization of 68017 in exponential form is:

68017 = 17¹ × 4001¹

Step-3: Factors of 68000

List of positive integer factors of 68000 that divides 68000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 68, 80, 85, 100, 125, 136, 160, 170, 200, 250, 272, 340, 400, 425, 500, 544, 680, 800, 850, 1000, 1360, 1700, 2000, 2125, 2720, 3400, 4000, 4250, 6800, 8500, 13600, 17000, 34000

Step-4: Factors of 68017

List of positive integer factors of 68017 that divides 68000 without a remainder.

1, 17, 4001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 68000 and 68017. The biggest common factor number is the GCF number.
So the greatest common factor 68000 and 68017 is 17.

Also check out the Least Common Multiple of 68000 and 68017