What is the Greatest Common Factor of 76314 and 76329?

Greatest common factor (GCF) of 76314 and 76329 is 3.

GCF(76314,76329) = 3

We will now calculate the prime factors of 76314 and 76329, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76314 and 76329.

How to find the GCF of 76314 and 76329?

We will first find the prime factorization of 76314 and 76329. After we will calculate the factors of 76314 and 76329 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 76329

Prime factors of 76329 are 3, 11, 257. Prime factorization of 76329 in exponential form is:

76329 = 3³ × 11¹ × 257¹

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 76329

List of positive integer factors of 76329 that divides 76314 without a remainder.

1, 3, 9, 11, 27, 33, 99, 257, 297, 771, 2313, 2827, 6939, 8481, 25443

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76314 and 76329. The biggest common factor number is the GCF number.
So the greatest common factor 76314 and 76329 is 3.

Also check out the Least Common Multiple of 76314 and 76329