What is the Greatest Common Factor of 78144 and 78164?

Greatest common factor (GCF) of 78144 and 78164 is 4.

GCF(78144,78164) = 4

We will now calculate the prime factors of 78144 and 78164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78144 and 78164.

How to find the GCF of 78144 and 78164?

We will first find the prime factorization of 78144 and 78164. After we will calculate the factors of 78144 and 78164 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 78164

Prime factors of 78164 are 2, 19541. Prime factorization of 78164 in exponential form is:

78164 = 2² × 19541¹

Step-3: Factors of 78144

List of positive integer factors of 78144 that divides 78144 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

Step-4: Factors of 78164

List of positive integer factors of 78164 that divides 78144 without a remainder.

1, 2, 4, 19541, 39082

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78144 and 78164. The biggest common factor number is the GCF number.
So the greatest common factor 78144 and 78164 is 4.

Also check out the Least Common Multiple of 78144 and 78164