What is the Greatest Common Factor of 48288 and 48300?

Greatest common factor (GCF) of 48288 and 48300 is 12.

GCF(48288,48300) = 12

We will now calculate the prime factors of 48288 and 48300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48288 and 48300.

How to find the GCF of 48288 and 48300?

We will first find the prime factorization of 48288 and 48300. After we will calculate the factors of 48288 and 48300 and find the biggest common factor number .

Step-1: Prime Factorization of 48288

Prime factors of 48288 are 2, 3, 503. Prime factorization of 48288 in exponential form is:

48288 = 2⁵ × 3¹ × 503¹

Step-2: Prime Factorization of 48300

Prime factors of 48300 are 2, 3, 5, 7, 23. Prime factorization of 48300 in exponential form is:

48300 = 2² × 3¹ × 5² × 7¹ × 23¹

Step-3: Factors of 48288

List of positive integer factors of 48288 that divides 48288 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 503, 1006, 1509, 2012, 3018, 4024, 6036, 8048, 12072, 16096, 24144

Step-4: Factors of 48300

List of positive integer factors of 48300 that divides 48288 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 23, 25, 28, 30, 35, 42, 46, 50, 60, 69, 70, 75, 84, 92, 100, 105, 115, 138, 140, 150, 161, 175, 210, 230, 276, 300, 322, 345, 350, 420, 460, 483, 525, 575, 644, 690, 700, 805, 966, 1050, 1150, 1380, 1610, 1725, 1932, 2100, 2300, 2415, 3220, 3450, 4025, 4830, 6900, 8050, 9660, 12075, 16100, 24150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48288 and 48300. The biggest common factor number is the GCF number.
So the greatest common factor 48288 and 48300 is 12.

Also check out the Least Common Multiple of 48288 and 48300