What is the Greatest Common Factor of 76320 and 76335?

Greatest common factor (GCF) of 76320 and 76335 is 15.

GCF(76320,76335) = 15

We will now calculate the prime factors of 76320 and 76335, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76320 and 76335.

How to find the GCF of 76320 and 76335?

We will first find the prime factorization of 76320 and 76335. After we will calculate the factors of 76320 and 76335 and find the biggest common factor number .

Step-1: Prime Factorization of 76320

Prime factors of 76320 are 2, 3, 5, 53. Prime factorization of 76320 in exponential form is:

76320 = 2⁵ × 3² × 5¹ × 53¹

Step-2: Prime Factorization of 76335

Prime factors of 76335 are 3, 5, 7, 727. Prime factorization of 76335 in exponential form is:

76335 = 3¹ × 5¹ × 7¹ × 727¹

Step-3: Factors of 76320

List of positive integer factors of 76320 that divides 76320 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 53, 60, 72, 80, 90, 96, 106, 120, 144, 159, 160, 180, 212, 240, 265, 288, 318, 360, 424, 477, 480, 530, 636, 720, 795, 848, 954, 1060, 1272, 1440, 1590, 1696, 1908, 2120, 2385, 2544, 3180, 3816, 4240, 4770, 5088, 6360, 7632, 8480, 9540, 12720, 15264, 19080, 25440, 38160

Step-4: Factors of 76335

List of positive integer factors of 76335 that divides 76320 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 727, 2181, 3635, 5089, 10905, 15267, 25445

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76320 and 76335. The biggest common factor number is the GCF number.
So the greatest common factor 76320 and 76335 is 15.

Also check out the Least Common Multiple of 76320 and 76335