What is the Greatest Common Factor of 5306 and 5312?

Greatest common factor (GCF) of 5306 and 5312 is 2.

GCF(5306,5312) = 2

We will now calculate the prime factors of 5306 and 5312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5306 and 5312.

How to find the GCF of 5306 and 5312?

We will first find the prime factorization of 5306 and 5312. After we will calculate the factors of 5306 and 5312 and find the biggest common factor number .

Step-1: Prime Factorization of 5306

Prime factors of 5306 are 2, 7, 379. Prime factorization of 5306 in exponential form is:

5306 = 2¹ × 7¹ × 379¹

Step-2: Prime Factorization of 5312

Prime factors of 5312 are 2, 83. Prime factorization of 5312 in exponential form is:

5312 = 2⁶ × 83¹

Step-3: Factors of 5306

List of positive integer factors of 5306 that divides 5306 without a remainder.

1, 2, 7, 14, 379, 758, 2653

Step-4: Factors of 5312

List of positive integer factors of 5312 that divides 5306 without a remainder.

1, 2, 4, 8, 16, 32, 64, 83, 166, 332, 664, 1328, 2656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5306 and 5312. The biggest common factor number is the GCF number.
So the greatest common factor 5306 and 5312 is 2.

Also check out the Least Common Multiple of 5306 and 5312