What is the Greatest Common Factor of 30000 and 30009?

Greatest common factor (GCF) of 30000 and 30009 is 3.

GCF(30000,30009) = 3

We will now calculate the prime factors of 30000 and 30009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30000 and 30009.

How to find the GCF of 30000 and 30009?

We will first find the prime factorization of 30000 and 30009. After we will calculate the factors of 30000 and 30009 and find the biggest common factor number .

Step-1: Prime Factorization of 30000

Prime factors of 30000 are 2, 3, 5. Prime factorization of 30000 in exponential form is:

30000 = 2⁴ × 3¹ × 5⁴

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 30000

List of positive integer factors of 30000 that divides 30000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 625, 750, 1000, 1200, 1250, 1500, 1875, 2000, 2500, 3000, 3750, 5000, 6000, 7500, 10000, 15000

Step-4: Factors of 30009

List of positive integer factors of 30009 that divides 30000 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30000 and 30009. The biggest common factor number is the GCF number.
So the greatest common factor 30000 and 30009 is 3.

Also check out the Least Common Multiple of 30000 and 30009