What is the Greatest Common Factor of 74000 and 74008?

Greatest common factor (GCF) of 74000 and 74008 is 8.

GCF(74000,74008) = 8

We will now calculate the prime factors of 74000 and 74008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74000 and 74008.

How to find the GCF of 74000 and 74008?

We will first find the prime factorization of 74000 and 74008. After we will calculate the factors of 74000 and 74008 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 74008

Prime factors of 74008 are 2, 11, 29. Prime factorization of 74008 in exponential form is:

74008 = 2³ × 11¹ × 29²

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 74008

List of positive integer factors of 74008 that divides 74000 without a remainder.

1, 2, 4, 8, 11, 22, 29, 44, 58, 88, 116, 232, 319, 638, 841, 1276, 1682, 2552, 3364, 6728, 9251, 18502, 37004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74000 and 74008. The biggest common factor number is the GCF number.
So the greatest common factor 74000 and 74008 is 8.

Also check out the Least Common Multiple of 74000 and 74008