What is the Greatest Common Factor of 53280 and 53300?

Greatest common factor (GCF) of 53280 and 53300 is 20.

GCF(53280,53300) = 20

We will now calculate the prime factors of 53280 and 53300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53280 and 53300.

How to find the GCF of 53280 and 53300?

We will first find the prime factorization of 53280 and 53300. After we will calculate the factors of 53280 and 53300 and find the biggest common factor number .

Step-1: Prime Factorization of 53280

Prime factors of 53280 are 2, 3, 5, 37. Prime factorization of 53280 in exponential form is:

53280 = 2⁵ × 3² × 5¹ × 37¹

Step-2: Prime Factorization of 53300

Prime factors of 53300 are 2, 5, 13, 41. Prime factorization of 53300 in exponential form is:

53300 = 2² × 5² × 13¹ × 41¹

Step-3: Factors of 53280

List of positive integer factors of 53280 that divides 53280 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 37, 40, 45, 48, 60, 72, 74, 80, 90, 96, 111, 120, 144, 148, 160, 180, 185, 222, 240, 288, 296, 333, 360, 370, 444, 480, 555, 592, 666, 720, 740, 888, 1110, 1184, 1332, 1440, 1480, 1665, 1776, 2220, 2664, 2960, 3330, 3552, 4440, 5328, 5920, 6660, 8880, 10656, 13320, 17760, 26640

Step-4: Factors of 53300

List of positive integer factors of 53300 that divides 53280 without a remainder.

1, 2, 4, 5, 10, 13, 20, 25, 26, 41, 50, 52, 65, 82, 100, 130, 164, 205, 260, 325, 410, 533, 650, 820, 1025, 1066, 1300, 2050, 2132, 2665, 4100, 5330, 10660, 13325, 26650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53280 and 53300. The biggest common factor number is the GCF number.
So the greatest common factor 53280 and 53300 is 20.

Also check out the Least Common Multiple of 53280 and 53300