What is the Greatest Common Factor of 29997 and 30008?

Greatest common factor (GCF) of 29997 and 30008 is 11.

GCF(29997,30008) = 11

We will now calculate the prime factors of 29997 and 30008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29997 and 30008.

How to find the GCF of 29997 and 30008?

We will first find the prime factorization of 29997 and 30008. After we will calculate the factors of 29997 and 30008 and find the biggest common factor number .

Step-1: Prime Factorization of 29997

Prime factors of 29997 are 3, 11, 101. Prime factorization of 29997 in exponential form is:

29997 = 3³ × 11¹ × 101¹

Step-2: Prime Factorization of 30008

Prime factors of 30008 are 2, 11, 31. Prime factorization of 30008 in exponential form is:

30008 = 2³ × 11² × 31¹

Step-3: Factors of 29997

List of positive integer factors of 29997 that divides 29997 without a remainder.

1, 3, 9, 11, 27, 33, 99, 101, 297, 303, 909, 1111, 2727, 3333, 9999

Step-4: Factors of 30008

List of positive integer factors of 30008 that divides 29997 without a remainder.

1, 2, 4, 8, 11, 22, 31, 44, 62, 88, 121, 124, 242, 248, 341, 484, 682, 968, 1364, 2728, 3751, 7502, 15004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29997 and 30008. The biggest common factor number is the GCF number.
So the greatest common factor 29997 and 30008 is 11.

Also check out the Least Common Multiple of 29997 and 30008