What is the Greatest Common Factor of 73986 and 74005?

Greatest common factor (GCF) of 73986 and 74005 is 19.

GCF(73986,74005) = 19

We will now calculate the prime factors of 73986 and 74005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73986 and 74005.

How to find the GCF of 73986 and 74005?

We will first find the prime factorization of 73986 and 74005. After we will calculate the factors of 73986 and 74005 and find the biggest common factor number .

Step-1: Prime Factorization of 73986

Prime factors of 73986 are 2, 3, 11, 19, 59. Prime factorization of 73986 in exponential form is:

73986 = 2¹ × 3¹ × 11¹ × 19¹ × 59¹

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 73986

List of positive integer factors of 73986 that divides 73986 without a remainder.

1, 2, 3, 6, 11, 19, 22, 33, 38, 57, 59, 66, 114, 118, 177, 209, 354, 418, 627, 649, 1121, 1254, 1298, 1947, 2242, 3363, 3894, 6726, 12331, 24662, 36993

Step-4: Factors of 74005

List of positive integer factors of 74005 that divides 73986 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 73986 and 74005. The biggest common factor number is the GCF number.
So the greatest common factor 73986 and 74005 is 19.

Also check out the Least Common Multiple of 73986 and 74005