What is the Greatest Common Factor of 34000 and 34012?

Greatest common factor (GCF) of 34000 and 34012 is 4.

GCF(34000,34012) = 4

We will now calculate the prime factors of 34000 and 34012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34000 and 34012.

How to find the GCF of 34000 and 34012?

We will first find the prime factorization of 34000 and 34012. After we will calculate the factors of 34000 and 34012 and find the biggest common factor number .

Step-1: Prime Factorization of 34000

Prime factors of 34000 are 2, 5, 17. Prime factorization of 34000 in exponential form is:

34000 = 2⁴ × 5³ × 17¹

Step-2: Prime Factorization of 34012

Prime factors of 34012 are 2, 11, 773. Prime factorization of 34012 in exponential form is:

34012 = 2² × 11¹ × 773¹

Step-3: Factors of 34000

List of positive integer factors of 34000 that divides 34000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 34, 40, 50, 68, 80, 85, 100, 125, 136, 170, 200, 250, 272, 340, 400, 425, 500, 680, 850, 1000, 1360, 1700, 2000, 2125, 3400, 4250, 6800, 8500, 17000

Step-4: Factors of 34012

List of positive integer factors of 34012 that divides 34000 without a remainder.

1, 2, 4, 11, 22, 44, 773, 1546, 3092, 8503, 17006

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34000 and 34012. The biggest common factor number is the GCF number.
So the greatest common factor 34000 and 34012 is 4.

Also check out the Least Common Multiple of 34000 and 34012