What is the Greatest Common Factor of 67000 and 67014?

Greatest common factor (GCF) of 67000 and 67014 is 2.

GCF(67000,67014) = 2

We will now calculate the prime factors of 67000 and 67014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67000 and 67014.

How to find the GCF of 67000 and 67014?

We will first find the prime factorization of 67000 and 67014. After we will calculate the factors of 67000 and 67014 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 67014

Prime factors of 67014 are 2, 3, 17, 73. Prime factorization of 67014 in exponential form is:

67014 = 2¹ × 3³ × 17¹ × 73¹

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 67014

List of positive integer factors of 67014 that divides 67000 without a remainder.

1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 73, 102, 146, 153, 219, 306, 438, 459, 657, 918, 1241, 1314, 1971, 2482, 3723, 3942, 7446, 11169, 22338, 33507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67000 and 67014. The biggest common factor number is the GCF number.
So the greatest common factor 67000 and 67014 is 2.

Also check out the Least Common Multiple of 67000 and 67014