What is the Greatest Common Factor of 30000 and 30012?

Greatest common factor (GCF) of 30000 and 30012 is 12.

GCF(30000,30012) = 12

We will now calculate the prime factors of 30000 and 30012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30000 and 30012.

How to find the GCF of 30000 and 30012?

We will first find the prime factorization of 30000 and 30012. After we will calculate the factors of 30000 and 30012 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 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 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 30012

List of positive integer factors of 30012 that divides 30000 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 30000 and 30012. The biggest common factor number is the GCF number.
So the greatest common factor 30000 and 30012 is 12.

Also check out the Least Common Multiple of 30000 and 30012