What is the Greatest Common Factor of 5280 and 5300?

Greatest common factor (GCF) of 5280 and 5300 is 20.

GCF(5280,5300) = 20

We will now calculate the prime factors of 5280 and 5300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5280 and 5300.

How to find the GCF of 5280 and 5300?

We will first find the prime factorization of 5280 and 5300. After we will calculate the factors of 5280 and 5300 and find the biggest common factor number .

Step-1: Prime Factorization of 5280

Prime factors of 5280 are 2, 3, 5, 11. Prime factorization of 5280 in exponential form is:

5280 = 2⁵ × 3¹ × 5¹ × 11¹

Step-2: Prime Factorization of 5300

Prime factors of 5300 are 2, 5, 53. Prime factorization of 5300 in exponential form is:

5300 = 2² × 5² × 53¹

Step-3: Factors of 5280

List of positive integer factors of 5280 that divides 5280 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 160, 165, 176, 220, 240, 264, 330, 352, 440, 480, 528, 660, 880, 1056, 1320, 1760, 2640

Step-4: Factors of 5300

List of positive integer factors of 5300 that divides 5280 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 53, 100, 106, 212, 265, 530, 1060, 1325, 2650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5280 and 5300. The biggest common factor number is the GCF number.
So the greatest common factor 5280 and 5300 is 20.

Also check out the Least Common Multiple of 5280 and 5300