What is the Greatest Common Factor of 76320 and 76330?

Greatest common factor (GCF) of 76320 and 76330 is 10.

GCF(76320,76330) = 10

We will now calculate the prime factors of 76320 and 76330, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76320 and 76330.

How to find the GCF of 76320 and 76330?

We will first find the prime factorization of 76320 and 76330. After we will calculate the factors of 76320 and 76330 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 76330

Prime factors of 76330 are 2, 5, 17, 449. Prime factorization of 76330 in exponential form is:

76330 = 2¹ × 5¹ × 17¹ × 449¹

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 76330

List of positive integer factors of 76330 that divides 76320 without a remainder.

1, 2, 5, 10, 17, 34, 85, 170, 449, 898, 2245, 4490, 7633, 15266, 38165

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76320 and 76330. The biggest common factor number is the GCF number.
So the greatest common factor 76320 and 76330 is 10.

Also check out the Least Common Multiple of 76320 and 76330