What is the Greatest Common Factor of 76305 and 76314?

Greatest common factor (GCF) of 76305 and 76314 is 3.

GCF(76305,76314) = 3

We will now calculate the prime factors of 76305 and 76314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76305 and 76314.

How to find the GCF of 76305 and 76314?

We will first find the prime factorization of 76305 and 76314. After we will calculate the factors of 76305 and 76314 and find the biggest common factor number .

Step-1: Prime Factorization of 76305

Prime factors of 76305 are 3, 5, 5087. Prime factorization of 76305 in exponential form is:

76305 = 3¹ × 5¹ × 5087¹

Step-2: 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-3: Factors of 76305

List of positive integer factors of 76305 that divides 76305 without a remainder.

1, 3, 5, 15, 5087, 15261, 25435

Step-4: Factors of 76314

List of positive integer factors of 76314 that divides 76305 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76305 and 76314. The biggest common factor number is the GCF number.
So the greatest common factor 76305 and 76314 is 3.

Also check out the Least Common Multiple of 76305 and 76314