What is the Greatest Common Factor of 67000 and 67005?

Greatest common factor (GCF) of 67000 and 67005 is 5.

GCF(67000,67005) = 5

We will now calculate the prime factors of 67000 and 67005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67000 and 67005.

How to find the GCF of 67000 and 67005?

We will first find the prime factorization of 67000 and 67005. After we will calculate the factors of 67000 and 67005 and find the biggest common factor number .

Step-1: Prime Factorization of 67000

Prime factors of 67000 are 2, 5, 67. Prime factorization of 67000 in exponential form is:

67000 = 2³ × 5³ × 67¹

Step-2: Prime Factorization of 67005

Prime factors of 67005 are 3, 5, 1489. Prime factorization of 67005 in exponential form is:

67005 = 3² × 5¹ × 1489¹

Step-3: Factors of 67000

List of positive integer factors of 67000 that divides 67000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 67, 100, 125, 134, 200, 250, 268, 335, 500, 536, 670, 1000, 1340, 1675, 2680, 3350, 6700, 8375, 13400, 16750, 33500

Step-4: Factors of 67005

List of positive integer factors of 67005 that divides 67000 without a remainder.

1, 3, 5, 9, 15, 45, 1489, 4467, 7445, 13401, 22335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67000 and 67005. The biggest common factor number is the GCF number.
So the greatest common factor 67000 and 67005 is 5.

Also check out the Least Common Multiple of 67000 and 67005