What is the Greatest Common Factor of 75808 and 75816?

Greatest common factor (GCF) of 75808 and 75816 is 8.

GCF(75808,75816) = 8

We will now calculate the prime factors of 75808 and 75816, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75808 and 75816.

How to find the GCF of 75808 and 75816?

We will first find the prime factorization of 75808 and 75816. After we will calculate the factors of 75808 and 75816 and find the biggest common factor number .

Step-1: Prime Factorization of 75808

Prime factors of 75808 are 2, 23, 103. Prime factorization of 75808 in exponential form is:

75808 = 2⁵ × 23¹ × 103¹

Step-2: Prime Factorization of 75816

Prime factors of 75816 are 2, 3, 13. Prime factorization of 75816 in exponential form is:

75816 = 2³ × 3⁶ × 13¹

Step-3: Factors of 75808

List of positive integer factors of 75808 that divides 75808 without a remainder.

1, 2, 4, 8, 16, 23, 32, 46, 92, 103, 184, 206, 368, 412, 736, 824, 1648, 2369, 3296, 4738, 9476, 18952, 37904

Step-4: Factors of 75816

List of positive integer factors of 75816 that divides 75808 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 27, 36, 39, 52, 54, 72, 78, 81, 104, 108, 117, 156, 162, 216, 234, 243, 312, 324, 351, 468, 486, 648, 702, 729, 936, 972, 1053, 1404, 1458, 1944, 2106, 2808, 2916, 3159, 4212, 5832, 6318, 8424, 9477, 12636, 18954, 25272, 37908

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75808 and 75816. The biggest common factor number is the GCF number.
So the greatest common factor 75808 and 75816 is 8.

Also check out the Least Common Multiple of 75808 and 75816