What is the Greatest Common Factor of 68000 and 68005?

Greatest common factor (GCF) of 68000 and 68005 is 5.

GCF(68000,68005) = 5

We will now calculate the prime factors of 68000 and 68005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 68000 and 68005.

How to find the GCF of 68000 and 68005?

We will first find the prime factorization of 68000 and 68005. After we will calculate the factors of 68000 and 68005 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 68005

Prime factors of 68005 are 5, 7, 29, 67. Prime factorization of 68005 in exponential form is:

68005 = 5¹ × 7¹ × 29¹ × 67¹

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 68005

List of positive integer factors of 68005 that divides 68000 without a remainder.

1, 5, 7, 29, 35, 67, 145, 203, 335, 469, 1015, 1943, 2345, 9715, 13601

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 68000 and 68005. The biggest common factor number is the GCF number.
So the greatest common factor 68000 and 68005 is 5.

Also check out the Least Common Multiple of 68000 and 68005