What is the Greatest Common Factor of 78128 and 78144?

Greatest common factor (GCF) of 78128 and 78144 is 16.

GCF(78128,78144) = 16

We will now calculate the prime factors of 78128 and 78144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78128 and 78144.

How to find the GCF of 78128 and 78144?

We will first find the prime factorization of 78128 and 78144. After we will calculate the factors of 78128 and 78144 and find the biggest common factor number .

Step-1: Prime Factorization of 78128

Prime factors of 78128 are 2, 19, 257. Prime factorization of 78128 in exponential form is:

78128 = 2⁴ × 19¹ × 257¹

Step-2: Prime Factorization of 78144

Prime factors of 78144 are 2, 3, 11, 37. Prime factorization of 78144 in exponential form is:

78144 = 2⁶ × 3¹ × 11¹ × 37¹

Step-3: Factors of 78128

List of positive integer factors of 78128 that divides 78128 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 152, 257, 304, 514, 1028, 2056, 4112, 4883, 9766, 19532, 39064

Step-4: Factors of 78144

List of positive integer factors of 78144 that divides 78128 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 37, 44, 48, 64, 66, 74, 88, 96, 111, 132, 148, 176, 192, 222, 264, 296, 352, 407, 444, 528, 592, 704, 814, 888, 1056, 1184, 1221, 1628, 1776, 2112, 2368, 2442, 3256, 3552, 4884, 6512, 7104, 9768, 13024, 19536, 26048, 39072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78128 and 78144. The biggest common factor number is the GCF number.
So the greatest common factor 78128 and 78144 is 16.

Also check out the Least Common Multiple of 78128 and 78144