What is the Greatest Common Factor of 76314 and 76320?

Greatest common factor (GCF) of 76314 and 76320 is 6.

GCF(76314,76320) = 6

We will now calculate the prime factors of 76314 and 76320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76314 and 76320.

How to find the GCF of 76314 and 76320?

We will first find the prime factorization of 76314 and 76320. After we will calculate the factors of 76314 and 76320 and find the biggest common factor number .

Step-1: Prime Factorization of 76314

Prime factors of 76314 are 2, 3, 7, 23, 79. Prime factorization of 76314 in exponential form is:

76314 = 2¹ × 3¹ × 7¹ × 23¹ × 79¹

Step-2: 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-3: Factors of 76314

List of positive integer factors of 76314 that divides 76314 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 79, 138, 158, 161, 237, 322, 474, 483, 553, 966, 1106, 1659, 1817, 3318, 3634, 5451, 10902, 12719, 25438, 38157

Step-4: Factors of 76320

List of positive integer factors of 76320 that divides 76314 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76314 and 76320. The biggest common factor number is the GCF number.
So the greatest common factor 76314 and 76320 is 6.

Also check out the Least Common Multiple of 76314 and 76320