What is the Greatest Common Factor of 74000 and 74005?

Greatest common factor (GCF) of 74000 and 74005 is 5.

GCF(74000,74005) = 5

We will now calculate the prime factors of 74000 and 74005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74000 and 74005.

How to find the GCF of 74000 and 74005?

We will first find the prime factorization of 74000 and 74005. After we will calculate the factors of 74000 and 74005 and find the biggest common factor number .

Step-1: Prime Factorization of 74000

Prime factors of 74000 are 2, 5, 37. Prime factorization of 74000 in exponential form is:

74000 = 2⁴ × 5³ × 37¹

Step-2: Prime Factorization of 74005

Prime factors of 74005 are 5, 19, 41. Prime factorization of 74005 in exponential form is:

74005 = 5¹ × 19² × 41¹

Step-3: Factors of 74000

List of positive integer factors of 74000 that divides 74000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 37, 40, 50, 74, 80, 100, 125, 148, 185, 200, 250, 296, 370, 400, 500, 592, 740, 925, 1000, 1480, 1850, 2000, 2960, 3700, 4625, 7400, 9250, 14800, 18500, 37000

Step-4: Factors of 74005

List of positive integer factors of 74005 that divides 74000 without a remainder.

1, 5, 19, 41, 95, 205, 361, 779, 1805, 3895, 14801

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74000 and 74005. The biggest common factor number is the GCF number.
So the greatest common factor 74000 and 74005 is 5.

Also check out the Least Common Multiple of 74000 and 74005