What is the Greatest Common Factor of 30128 and 30140?

Greatest common factor (GCF) of 30128 and 30140 is 4.

GCF(30128,30140) = 4

We will now calculate the prime factors of 30128 and 30140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30128 and 30140.

How to find the GCF of 30128 and 30140?

We will first find the prime factorization of 30128 and 30140. After we will calculate the factors of 30128 and 30140 and find the biggest common factor number .

Step-1: Prime Factorization of 30128

Prime factors of 30128 are 2, 7, 269. Prime factorization of 30128 in exponential form is:

30128 = 2⁴ × 7¹ × 269¹

Step-2: Prime Factorization of 30140

Prime factors of 30140 are 2, 5, 11, 137. Prime factorization of 30140 in exponential form is:

30140 = 2² × 5¹ × 11¹ × 137¹

Step-3: Factors of 30128

List of positive integer factors of 30128 that divides 30128 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 269, 538, 1076, 1883, 2152, 3766, 4304, 7532, 15064

Step-4: Factors of 30140

List of positive integer factors of 30140 that divides 30128 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 137, 220, 274, 548, 685, 1370, 1507, 2740, 3014, 6028, 7535, 15070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30128 and 30140. The biggest common factor number is the GCF number.
So the greatest common factor 30128 and 30140 is 4.

Also check out the Least Common Multiple of 30128 and 30140