What is the Greatest Common Factor of 29997 and 30009?

Greatest common factor (GCF) of 29997 and 30009 is 3.

GCF(29997,30009) = 3

We will now calculate the prime factors of 29997 and 30009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29997 and 30009.

How to find the GCF of 29997 and 30009?

We will first find the prime factorization of 29997 and 30009. After we will calculate the factors of 29997 and 30009 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 30009

Prime factors of 30009 are 3, 7, 1429. Prime factorization of 30009 in exponential form is:

30009 = 3¹ × 7¹ × 1429¹

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 30009

List of positive integer factors of 30009 that divides 29997 without a remainder.

1, 3, 7, 21, 1429, 4287, 10003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29997 and 30009. The biggest common factor number is the GCF number.
So the greatest common factor 29997 and 30009 is 3.

Also check out the Least Common Multiple of 29997 and 30009