What is the Greatest Common Factor of 5314 and 5328?

Greatest common factor (GCF) of 5314 and 5328 is 2.

GCF(5314,5328) = 2

We will now calculate the prime factors of 5314 and 5328, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5314 and 5328.

How to find the GCF of 5314 and 5328?

We will first find the prime factorization of 5314 and 5328. After we will calculate the factors of 5314 and 5328 and find the biggest common factor number .

Step-1: Prime Factorization of 5314

Prime factors of 5314 are 2, 2657. Prime factorization of 5314 in exponential form is:

5314 = 2¹ × 2657¹

Step-2: Prime Factorization of 5328

Prime factors of 5328 are 2, 3, 37. Prime factorization of 5328 in exponential form is:

5328 = 2⁴ × 3² × 37¹

Step-3: Factors of 5314

List of positive integer factors of 5314 that divides 5314 without a remainder.

1, 2, 2657

Step-4: Factors of 5328

List of positive integer factors of 5328 that divides 5314 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 37, 48, 72, 74, 111, 144, 148, 222, 296, 333, 444, 592, 666, 888, 1332, 1776, 2664

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5314 and 5328. The biggest common factor number is the GCF number.
So the greatest common factor 5314 and 5328 is 2.

Also check out the Least Common Multiple of 5314 and 5328