What is the Greatest Common Factor of 29997 and 30012?

Greatest common factor (GCF) of 29997 and 30012 is 3.

GCF(29997,30012) = 3

We will now calculate the prime factors of 29997 and 30012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29997 and 30012.

How to find the GCF of 29997 and 30012?

We will first find the prime factorization of 29997 and 30012. After we will calculate the factors of 29997 and 30012 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 30012

Prime factors of 30012 are 2, 3, 41, 61. Prime factorization of 30012 in exponential form is:

30012 = 2² × 3¹ × 41¹ × 61¹

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 30012

List of positive integer factors of 30012 that divides 29997 without a remainder.

1, 2, 3, 4, 6, 12, 41, 61, 82, 122, 123, 164, 183, 244, 246, 366, 492, 732, 2501, 5002, 7503, 10004, 15006

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29997 and 30012. The biggest common factor number is the GCF number.
So the greatest common factor 29997 and 30012 is 3.

Also check out the Least Common Multiple of 29997 and 30012