What is the Greatest Common Factor of 73982 and 74000?

Greatest common factor (GCF) of 73982 and 74000 is 2.

GCF(73982,74000) = 2

We will now calculate the prime factors of 73982 and 74000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73982 and 74000.

How to find the GCF of 73982 and 74000?

We will first find the prime factorization of 73982 and 74000. After we will calculate the factors of 73982 and 74000 and find the biggest common factor number .

Step-1: Prime Factorization of 73982

Prime factors of 73982 are 2, 71, 521. Prime factorization of 73982 in exponential form is:

73982 = 2¹ × 71¹ × 521¹

Step-2: 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-3: Factors of 73982

List of positive integer factors of 73982 that divides 73982 without a remainder.

1, 2, 71, 142, 521, 1042, 36991

Step-4: Factors of 74000

List of positive integer factors of 74000 that divides 73982 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73982 and 74000. The biggest common factor number is the GCF number.
So the greatest common factor 73982 and 74000 is 2.

Also check out the Least Common Multiple of 73982 and 74000