What is the Greatest Common Factor of 77314 and 77322?

Greatest common factor (GCF) of 77314 and 77322 is 2.

GCF(77314,77322) = 2

We will now calculate the prime factors of 77314 and 77322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77314 and 77322.

How to find the GCF of 77314 and 77322?

We will first find the prime factorization of 77314 and 77322. After we will calculate the factors of 77314 and 77322 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 77322

Prime factors of 77322 are 2, 3, 7, 263. Prime factorization of 77322 in exponential form is:

77322 = 2¹ × 3¹ × 7² × 263¹

Step-3: Factors of 77314

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

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

Step-4: Factors of 77322

List of positive integer factors of 77322 that divides 77314 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 263, 294, 526, 789, 1578, 1841, 3682, 5523, 11046, 12887, 25774, 38661

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77314 and 77322. The biggest common factor number is the GCF number.
So the greatest common factor 77314 and 77322 is 2.

Also check out the Least Common Multiple of 77314 and 77322