What is the Greatest Common Factor of 30000 and 30006?

Greatest common factor (GCF) of 30000 and 30006 is 6.

GCF(30000,30006) = 6

We will now calculate the prime factors of 30000 and 30006, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30000 and 30006.

How to find the GCF of 30000 and 30006?

We will first find the prime factorization of 30000 and 30006. After we will calculate the factors of 30000 and 30006 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 30006

Prime factors of 30006 are 2, 3, 1667. Prime factorization of 30006 in exponential form is:

30006 = 2¹ × 3² × 1667¹

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 30006

List of positive integer factors of 30006 that divides 30000 without a remainder.

1, 2, 3, 6, 9, 18, 1667, 3334, 5001, 10002, 15003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30000 and 30006. The biggest common factor number is the GCF number.
So the greatest common factor 30000 and 30006 is 6.

Also check out the Least Common Multiple of 30000 and 30006