What is the Greatest Common Factor of 37990 and 38000?

Greatest common factor (GCF) of 37990 and 38000 is 10.

GCF(37990,38000) = 10

We will now calculate the prime factors of 37990 and 38000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37990 and 38000.

How to find the GCF of 37990 and 38000?

We will first find the prime factorization of 37990 and 38000. After we will calculate the factors of 37990 and 38000 and find the biggest common factor number .

Step-1: Prime Factorization of 37990

Prime factors of 37990 are 2, 5, 29, 131. Prime factorization of 37990 in exponential form is:

37990 = 2¹ × 5¹ × 29¹ × 131¹

Step-2: 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-3: Factors of 37990

List of positive integer factors of 37990 that divides 37990 without a remainder.

1, 2, 5, 10, 29, 58, 131, 145, 262, 290, 655, 1310, 3799, 7598, 18995

Step-4: Factors of 38000

List of positive integer factors of 38000 that divides 37990 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37990 and 38000. The biggest common factor number is the GCF number.
So the greatest common factor 37990 and 38000 is 10.

Also check out the Least Common Multiple of 37990 and 38000