What is the Greatest Common Factor of 38000 and 38014?

Greatest common factor (GCF) of 38000 and 38014 is 2.

GCF(38000,38014) = 2

We will now calculate the prime factors of 38000 and 38014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38000 and 38014.

How to find the GCF of 38000 and 38014?

We will first find the prime factorization of 38000 and 38014. After we will calculate the factors of 38000 and 38014 and find the biggest common factor number .

Step-1: Prime Factorization of 38000

Prime factors of 38000 are 2, 5, 19. Prime factorization of 38000 in exponential form is:

38000 = 2⁴ × 5³ × 19¹

Step-2: Prime Factorization of 38014

Prime factors of 38014 are 2, 83, 229. Prime factorization of 38014 in exponential form is:

38014 = 2¹ × 83¹ × 229¹

Step-3: Factors of 38000

List of positive integer factors of 38000 that divides 38000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 25, 38, 40, 50, 76, 80, 95, 100, 125, 152, 190, 200, 250, 304, 380, 400, 475, 500, 760, 950, 1000, 1520, 1900, 2000, 2375, 3800, 4750, 7600, 9500, 19000

Step-4: Factors of 38014

List of positive integer factors of 38014 that divides 38000 without a remainder.

1, 2, 83, 166, 229, 458, 19007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38000 and 38014. The biggest common factor number is the GCF number.
So the greatest common factor 38000 and 38014 is 2.

Also check out the Least Common Multiple of 38000 and 38014