What is the Greatest Common Factor of 75816 and 75829?

Greatest common factor (GCF) of 75816 and 75829 is 13.

GCF(75816,75829) = 13

We will now calculate the prime factors of 75816 and 75829, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75816 and 75829.

How to find the GCF of 75816 and 75829?

We will first find the prime factorization of 75816 and 75829. After we will calculate the factors of 75816 and 75829 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75829

Prime factors of 75829 are 13, 19, 307. Prime factorization of 75829 in exponential form is:

75829 = 13¹ × 19¹ × 307¹

Step-3: Factors of 75816

List of positive integer factors of 75816 that divides 75816 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

Step-4: Factors of 75829

List of positive integer factors of 75829 that divides 75816 without a remainder.

1, 13, 19, 247, 307, 3991, 5833

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75816 and 75829. The biggest common factor number is the GCF number.
So the greatest common factor 75816 and 75829 is 13.

Also check out the Least Common Multiple of 75816 and 75829