What is the Greatest Common Factor of 5310 and 5328?

Greatest common factor (GCF) of 5310 and 5328 is 18.

GCF(5310,5328) = 18

We will now calculate the prime factors of 5310 and 5328, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5310 and 5328.

How to find the GCF of 5310 and 5328?

We will first find the prime factorization of 5310 and 5328. After we will calculate the factors of 5310 and 5328 and find the biggest common factor number .

Step-1: Prime Factorization of 5310

Prime factors of 5310 are 2, 3, 5, 59. Prime factorization of 5310 in exponential form is:

5310 = 2¹ × 3² × 5¹ × 59¹

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 5310

List of positive integer factors of 5310 that divides 5310 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 59, 90, 118, 177, 295, 354, 531, 590, 885, 1062, 1770, 2655

Step-4: Factors of 5328

List of positive integer factors of 5328 that divides 5310 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 5310 and 5328. The biggest common factor number is the GCF number.
So the greatest common factor 5310 and 5328 is 18.

Also check out the Least Common Multiple of 5310 and 5328