What is the Greatest Common Factor of 74000 and 74014?

Greatest common factor (GCF) of 74000 and 74014 is 2.

GCF(74000,74014) = 2

We will now calculate the prime factors of 74000 and 74014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74000 and 74014.

How to find the GCF of 74000 and 74014?

We will first find the prime factorization of 74000 and 74014. After we will calculate the factors of 74000 and 74014 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 74014

Prime factors of 74014 are 2, 23, 1609. Prime factorization of 74014 in exponential form is:

74014 = 2¹ × 23¹ × 1609¹

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 74014

List of positive integer factors of 74014 that divides 74000 without a remainder.

1, 2, 23, 46, 1609, 3218, 37007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74000 and 74014. The biggest common factor number is the GCF number.
So the greatest common factor 74000 and 74014 is 2.

Also check out the Least Common Multiple of 74000 and 74014