What is the Greatest Common Factor of 74000 and 74004?

Greatest common factor (GCF) of 74000 and 74004 is 4.

GCF(74000,74004) = 4

We will now calculate the prime factors of 74000 and 74004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74000 and 74004.

How to find the GCF of 74000 and 74004?

We will first find the prime factorization of 74000 and 74004. After we will calculate the factors of 74000 and 74004 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 74004

Prime factors of 74004 are 2, 3, 7, 881. Prime factorization of 74004 in exponential form is:

74004 = 2² × 3¹ × 7¹ × 881¹

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 74004

List of positive integer factors of 74004 that divides 74000 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 881, 1762, 2643, 3524, 5286, 6167, 10572, 12334, 18501, 24668, 37002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74000 and 74004. The biggest common factor number is the GCF number.
So the greatest common factor 74000 and 74004 is 4.

Also check out the Least Common Multiple of 74000 and 74004