What is the Greatest Common Factor of 78125 and 78144?

Greatest common factor (GCF) of 78125 and 78144 is 1.

GCF(78125,78144) = 1

We will now calculate the prime factors of 78125 and 78144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78125 and 78144.

How to find the GCF of 78125 and 78144?

We will first find the prime factorization of 78125 and 78144. After we will calculate the factors of 78125 and 78144 and find the biggest common factor number .

Step-1: Prime Factorization of 78125

Prime factors of 78125 are 5. Prime factorization of 78125 in exponential form is:

78125 = 5⁷

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 78125

List of positive integer factors of 78125 that divides 78125 without a remainder.

1, 5, 25, 125, 625, 3125, 15625

Step-4: Factors of 78144

List of positive integer factors of 78144 that divides 78125 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 78125 and 78144. The biggest common factor number is the GCF number.
So the greatest common factor 78125 and 78144 is 1.

Also check out the Least Common Multiple of 78125 and 78144