What is the Greatest Common Factor of 77296 and 77314?

Greatest common factor (GCF) of 77296 and 77314 is 2.

GCF(77296,77314) = 2

We will now calculate the prime factors of 77296 and 77314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77296 and 77314.

How to find the GCF of 77296 and 77314?

We will first find the prime factorization of 77296 and 77314. After we will calculate the factors of 77296 and 77314 and find the biggest common factor number .

Step-1: Prime Factorization of 77296

Prime factors of 77296 are 2, 4831. Prime factorization of 77296 in exponential form is:

77296 = 2⁴ × 4831¹

Step-2: Prime Factorization of 77314

Prime factors of 77314 are 2, 29, 31, 43. Prime factorization of 77314 in exponential form is:

77314 = 2¹ × 29¹ × 31¹ × 43¹

Step-3: Factors of 77296

List of positive integer factors of 77296 that divides 77296 without a remainder.

1, 2, 4, 8, 16, 4831, 9662, 19324, 38648

Step-4: Factors of 77314

List of positive integer factors of 77314 that divides 77296 without a remainder.

1, 2, 29, 31, 43, 58, 62, 86, 899, 1247, 1333, 1798, 2494, 2666, 38657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77296 and 77314. The biggest common factor number is the GCF number.
So the greatest common factor 77296 and 77314 is 2.

Also check out the Least Common Multiple of 77296 and 77314