What is the Greatest Common Factor of 30000 and 30016?

Greatest common factor (GCF) of 30000 and 30016 is 16.

GCF(30000,30016) = 16

We will now calculate the prime factors of 30000 and 30016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30000 and 30016.

How to find the GCF of 30000 and 30016?

We will first find the prime factorization of 30000 and 30016. After we will calculate the factors of 30000 and 30016 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 30016

Prime factors of 30016 are 2, 7, 67. Prime factorization of 30016 in exponential form is:

30016 = 2⁶ × 7¹ × 67¹

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 30016

List of positive integer factors of 30016 that divides 30000 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 67, 112, 134, 224, 268, 448, 469, 536, 938, 1072, 1876, 2144, 3752, 4288, 7504, 15008

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30000 and 30016. The biggest common factor number is the GCF number.
So the greatest common factor 30000 and 30016 is 16.

Also check out the Least Common Multiple of 30000 and 30016