What is the Greatest Common Factor of 39999 and 40005?

Greatest common factor (GCF) of 39999 and 40005 is 3.

GCF(39999,40005) = 3

We will now calculate the prime factors of 39999 and 40005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39999 and 40005.

How to find the GCF of 39999 and 40005?

We will first find the prime factorization of 39999 and 40005. After we will calculate the factors of 39999 and 40005 and find the biggest common factor number .

Step-1: Prime Factorization of 39999

Prime factors of 39999 are 3, 67, 199. Prime factorization of 39999 in exponential form is:

39999 = 3¹ × 67¹ × 199¹

Step-2: Prime Factorization of 40005

Prime factors of 40005 are 3, 5, 7, 127. Prime factorization of 40005 in exponential form is:

40005 = 3² × 5¹ × 7¹ × 127¹

Step-3: Factors of 39999

List of positive integer factors of 39999 that divides 39999 without a remainder.

1, 3, 67, 199, 201, 597, 13333

Step-4: Factors of 40005

List of positive integer factors of 40005 that divides 39999 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 127, 315, 381, 635, 889, 1143, 1905, 2667, 4445, 5715, 8001, 13335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39999 and 40005. The biggest common factor number is the GCF number.
So the greatest common factor 39999 and 40005 is 3.

Also check out the Least Common Multiple of 39999 and 40005