What is the Greatest Common Factor of 29997 and 30003?

Greatest common factor (GCF) of 29997 and 30003 is 3.

GCF(29997,30003) = 3

We will now calculate the prime factors of 29997 and 30003, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29997 and 30003.

How to find the GCF of 29997 and 30003?

We will first find the prime factorization of 29997 and 30003. After we will calculate the factors of 29997 and 30003 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 30003

Prime factors of 30003 are 3, 73, 137. Prime factorization of 30003 in exponential form is:

30003 = 3¹ × 73¹ × 137¹

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 30003

List of positive integer factors of 30003 that divides 29997 without a remainder.

1, 3, 73, 137, 219, 411, 10001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29997 and 30003. The biggest common factor number is the GCF number.
So the greatest common factor 29997 and 30003 is 3.

Also check out the Least Common Multiple of 29997 and 30003