What is the Greatest Common Factor of 30128 and 30144?

Greatest common factor (GCF) of 30128 and 30144 is 16.

GCF(30128,30144) = 16

We will now calculate the prime factors of 30128 and 30144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30128 and 30144.

How to find the GCF of 30128 and 30144?

We will first find the prime factorization of 30128 and 30144. After we will calculate the factors of 30128 and 30144 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 30144

Prime factors of 30144 are 2, 3, 157. Prime factorization of 30144 in exponential form is:

30144 = 2⁶ × 3¹ × 157¹

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 30144

List of positive integer factors of 30144 that divides 30128 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 157, 192, 314, 471, 628, 942, 1256, 1884, 2512, 3768, 5024, 7536, 10048, 15072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30128 and 30144. The biggest common factor number is the GCF number.
So the greatest common factor 30128 and 30144 is 16.

Also check out the Least Common Multiple of 30128 and 30144