What is the Greatest Common Factor of 5298 and 5312?

Greatest common factor (GCF) of 5298 and 5312 is 2.

GCF(5298,5312) = 2

We will now calculate the prime factors of 5298 and 5312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5298 and 5312.

How to find the GCF of 5298 and 5312?

We will first find the prime factorization of 5298 and 5312. After we will calculate the factors of 5298 and 5312 and find the biggest common factor number .

Step-1: Prime Factorization of 5298

Prime factors of 5298 are 2, 3, 883. Prime factorization of 5298 in exponential form is:

5298 = 2¹ × 3¹ × 883¹

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 5298

List of positive integer factors of 5298 that divides 5298 without a remainder.

1, 2, 3, 6, 883, 1766, 2649

Step-4: Factors of 5312

List of positive integer factors of 5312 that divides 5298 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 5298 and 5312. The biggest common factor number is the GCF number.
So the greatest common factor 5298 and 5312 is 2.

Also check out the Least Common Multiple of 5298 and 5312