What is the Greatest Common Factor of 67000 and 67008?

Greatest common factor (GCF) of 67000 and 67008 is 8.

GCF(67000,67008) = 8

We will now calculate the prime factors of 67000 and 67008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67000 and 67008.

How to find the GCF of 67000 and 67008?

We will first find the prime factorization of 67000 and 67008. After we will calculate the factors of 67000 and 67008 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 67008

Prime factors of 67008 are 2, 3, 349. Prime factorization of 67008 in exponential form is:

67008 = 2⁶ × 3¹ × 349¹

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 67008

List of positive integer factors of 67008 that divides 67000 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 349, 698, 1047, 1396, 2094, 2792, 4188, 5584, 8376, 11168, 16752, 22336, 33504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67000 and 67008. The biggest common factor number is the GCF number.
So the greatest common factor 67000 and 67008 is 8.

Also check out the Least Common Multiple of 67000 and 67008