What is the Greatest Common Factor of 34008 and 34014?

Greatest common factor (GCF) of 34008 and 34014 is 6.

GCF(34008,34014) = 6

We will now calculate the prime factors of 34008 and 34014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34008 and 34014.

How to find the GCF of 34008 and 34014?

We will first find the prime factorization of 34008 and 34014. After we will calculate the factors of 34008 and 34014 and find the biggest common factor number .

Step-1: Prime Factorization of 34008

Prime factors of 34008 are 2, 3, 13, 109. Prime factorization of 34008 in exponential form is:

34008 = 2³ × 3¹ × 13¹ × 109¹

Step-2: Prime Factorization of 34014

Prime factors of 34014 are 2, 3, 5669. Prime factorization of 34014 in exponential form is:

34014 = 2¹ × 3¹ × 5669¹

Step-3: Factors of 34008

List of positive integer factors of 34008 that divides 34008 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 109, 156, 218, 312, 327, 436, 654, 872, 1308, 1417, 2616, 2834, 4251, 5668, 8502, 11336, 17004

Step-4: Factors of 34014

List of positive integer factors of 34014 that divides 34008 without a remainder.

1, 2, 3, 6, 5669, 11338, 17007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34008 and 34014. The biggest common factor number is the GCF number.
So the greatest common factor 34008 and 34014 is 6.

Also check out the Least Common Multiple of 34008 and 34014